subject:(topological order)

1. Yang, Guang. Topological Order in Superconductors and Quantum Hall Liquids.

Degree: PhD, Physics, 2014, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:386208/

► Fractional quantum Hall (FQH) liquids are interesting two-dimensional electron systems that possess quasiparticle excitations with fractional charges, obeying quantum statistics different from those of bosons… (more)

▼ Fractional quantum Hall (FQH) liquids are interesting two-dimensional electron systems that possess quasiparticle excitations with fractional charges, obeying quantum statistics different from those of bosons and fermions. In particular, the FQH liquid at filling factor 5/2 was proposed to host Majorana bound state (MBS) with exotic non-Abelian statistics. A collection of MBSs can span a topological Hilbert space, in which each many-particle state is topologically distinct, depending on the historical trajectories of all the MBSs in the system. Logic operations in quantum computation can be encoded in the linear transformations in topological Hilbert space and in principle be protected against local defects and perturbations, which are topologically trivial and cannot induce transitions between different many-particle states. Despite such intriguing theoretical picture, experiments probing the nature of the 5/2 FQH liquid are controversial. In this dissertation, we provide an explanation of two seemingly contradicting experiments in the 5/2 FQH liquid, by exploring the role of electrostatic interaction closely related to the geometries of the devices. We also construct several new 5/2 FQH states, by making use of the particle-hole symmetry in FQH systems, to account for a recent experiment observing upstream neutral edge transport in the 5/2 FQH liquid, which ruled out most of the existing theories. In addition to the new particle-hole states, we propose another topological description of the 5/2 FQH liquid which reconciles all existing transport experiments. Later, we turn our attention to the MBSs in superconductor systems. We study the approaches to minimizing the decoherence of a Majorana-fermion-based qbit due to its interaction with environment, based on a full classification of the fermionic zero modes in a system of interacting Majorana fermions. Advisors/Committee Members: Feldman, Dmitri (Director), Kosterlitz, John (Reader), Mitrovic, Vesna (Reader).

Subjects/Keywords: topological order

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APA (6^th Edition):

Yang, G. (2014). Topological Order in Superconductors and Quantum Hall Liquids. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386208/

Chicago Manual of Style (16^th Edition):

Yang, Guang. “Topological Order in Superconductors and Quantum Hall Liquids.” 2014. Doctoral Dissertation, Brown University. Accessed January 26, 2021. https://repository.library.brown.edu/studio/item/bdr:386208/.

MLA Handbook (7^th Edition):

Yang, Guang. “Topological Order in Superconductors and Quantum Hall Liquids.” 2014. Web. 26 Jan 2021.

Vancouver:

Yang G. Topological Order in Superconductors and Quantum Hall Liquids. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2021 Jan 26]. Available from: https://repository.library.brown.edu/studio/item/bdr:386208/.

Council of Science Editors:

Yang G. Topological Order in Superconductors and Quantum Hall Liquids. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386208/

University of Toronto

2. Schaffer, Robert Stephen. Quantum Spin Liquids in Kitaev and Kagome Systems.

Degree: PhD, 2016, University of Toronto

URL: http://hdl.handle.net/1807/76836

► Quantum spin liquids, systems in which quantum fluctuations prevent the magnetic ordering of the spin degrees of freedom down to zero temperature, have been the… (more)

▼ Quantum spin liquids, systems in which quantum fluctuations prevent the magnetic ordering of the spin degrees of freedom down to zero temperature, have been the source of much recent theoretical and experimental interest. These systems are characterised by their long ranged entangled states, preserve symmetries down to zero Kelvin, and have been shown to exhibit fascinating properties such as a topological ground state degeneracy and fractionalised spin excitations. In this thesis, we study several of these phases. The first, Kitaev spin liquids, appear in strongly spin-orbit coupled systems, where the SU(2) spin symmetry is broken. Within our mean field approach, we study the quantum phase transition from the gapless Z₂ spin liquid to a magnetically ordered phase within the Heisenberg-Kitaev model. Beyond the mean field theory, we argue that the gauge structure of the spin liquid plays a crucial role in this transition, leading to a confinement of spinons and the generation of magnetic order. We also discuss the three-dimensional iridate compounds, where the Kitaev spin liquid phase has topologically protected bulk and surface excitations. We next discuss spin liquids appearing on the geometrically frustrated kagome lattice. First, we consider non-Kramers spin liquids, in which the spin structure of the theory is protected by lattice, rather than time-reversal, symmetry. As a result, more phases are allowed, which have different properties than those which transform as Kramers doublets. In addition, these may have positive experimental signatures in the Raman scattering intensity, offering a clear path to detect such a state. Finally, we examine possible spin liquid phases on a breathing kagome lattice, where we find a stable Z₂ spin liquid to be the ground state. This may help to guide future numerical studies of the kagome lattice Heisenberg model, and may also be relevant to DQVOF, a recently discovered spin liquid candidate compound. Advisors/Committee Members: Kim, Yong Baek, Physics.

Subjects/Keywords: Spin Liquids; Topological Order; 0605

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Schaffer, R. S. (2016). Quantum Spin Liquids in Kitaev and Kagome Systems. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/76836

Chicago Manual of Style (16^th Edition):

Schaffer, Robert Stephen. “Quantum Spin Liquids in Kitaev and Kagome Systems.” 2016. Doctoral Dissertation, University of Toronto. Accessed January 26, 2021. http://hdl.handle.net/1807/76836.

MLA Handbook (7^th Edition):

Schaffer, Robert Stephen. “Quantum Spin Liquids in Kitaev and Kagome Systems.” 2016. Web. 26 Jan 2021.

Vancouver:

Schaffer RS. Quantum Spin Liquids in Kitaev and Kagome Systems. [Internet] [Doctoral dissertation]. University of Toronto; 2016. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1807/76836.

Council of Science Editors:

Schaffer RS. Quantum Spin Liquids in Kitaev and Kagome Systems. [Doctoral Dissertation]. University of Toronto; 2016. Available from: http://hdl.handle.net/1807/76836

University of Southern California

3. Santra, Siddhartha. Quantum information techniques in condensed matter: quantum equilibration, entanglement typicality, detection of topological order.

Degree: PhD, Physics, 2014, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/381855/rec/5366

► This thesis presents insights obtained on three questions in condensed matter physics via techniques in quantum information. ❧ The first topic deals with signatures of… (more)

▼ This thesis presents insights obtained on three questions in condensed matter physics via techniques in quantum information. ❧ The first topic deals with signatures of equilibration in a closed quantum system. Using the Loschmidt echo as a representative observable, that is derived from fidelity—a popular quantity in quantum information, and by studying it's long time statistics the role of quantum criticality in the equilibration dynamics of a closed system is analysed. While off‐critical systems under a quantum quench are shown to equilibrate well, critical systems are shown to do so poorly signified by relatively large fluctuations of the echo around it’s long time average. ❧ The second topic deals with typicality of entanglement in the physical Hilbert space. Here, a general framework for studying statistical moments of physically relevant quantities in ensembles of quantum states generated by Local Random Quantum Circuits (LRQC) is outlined. These ensembles are constructed by finite‐length random quantum circuits acting on the (hyper)edges of an underlying (hyper)graph structure. The latter are designed to encode for the locality structure associated with finite‐time quantum evolutions generated by physical i.e. local Hamiltonians. Physical properties of typical states in these ensembles, in particular purity as a proxy of quantum entanglement is studied. The problem is formulated in terms of matrix elements of superoperators which depend on the graph structure, choice of probability measure over the local unitaries and circuit length. We consider different families of LRQCs and study their typical entanglement properties for finite‐time as well as their asymptotic behavior. In particular, for a model of LRQC that resembles closely the Trotter scheme of discretizing quantum evolutions with local Hamiltonians, we find that the area law holds in average and that the volume law is a typical property (that is, it holds in average and the fluctuations around the average are vanishing for the large system) of physical states. The area law arises when the evolution time is O(1) with respect to the size L of the system, while the volume law arises as typical when the evolution time scales like O(L). ❧ The final topic deals with the perturbative response of the set of Rényi entropies of a subsystem when the entire system is in a state displaying some quantum order. The characteristic behavior of the entropies is shown to be able to identify topologically non‐trivial and trivial phases in the case of quantum double models. The implications of the response towards the possibility of simulating the adiabatic evolution within a phase using the protocol of Local Operations and Classical Communications are discussed. Advisors/Committee Members: Zanardi, Paolo (Committee Chair), Lidar, Daniel A. (Committee Member), Brun, Todd A. (Committee Member), Campos Venuti, Lorenzo (Committee Member), Jonckheere, Edmond A. (Committee Member).

Subjects/Keywords: quantum information; equilibration; entanglement; topological order

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APA (6^th Edition):

Santra, S. (2014). Quantum information techniques in condensed matter: quantum equilibration, entanglement typicality, detection of topological order. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/381855/rec/5366

Chicago Manual of Style (16^th Edition):

Santra, Siddhartha. “Quantum information techniques in condensed matter: quantum equilibration, entanglement typicality, detection of topological order.” 2014. Doctoral Dissertation, University of Southern California. Accessed January 26, 2021. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/381855/rec/5366.

MLA Handbook (7^th Edition):

Santra, Siddhartha. “Quantum information techniques in condensed matter: quantum equilibration, entanglement typicality, detection of topological order.” 2014. Web. 26 Jan 2021.

Vancouver:

Santra S. Quantum information techniques in condensed matter: quantum equilibration, entanglement typicality, detection of topological order. [Internet] [Doctoral dissertation]. University of Southern California; 2014. [cited 2021 Jan 26]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/381855/rec/5366.

Council of Science Editors:

Santra S. Quantum information techniques in condensed matter: quantum equilibration, entanglement typicality, detection of topological order. [Doctoral Dissertation]. University of Southern California; 2014. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/381855/rec/5366

University of Sydney

4. Brell, Courtney Gordon Gray. Many-body models for topological quantum information .

Degree: 2014, University of Sydney

URL: http://hdl.handle.net/2123/13539

► We develop and investigate several quantum many-body spin models of use for topological quantum information processing and storage. These models fall into two categories: those… (more)

Subjects/Keywords: quantum computation; topological order; many-body physics

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APA (6^th Edition):

Brell, C. G. G. (2014). Many-body models for topological quantum information . (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/13539

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Brell, Courtney Gordon Gray. “Many-body models for topological quantum information .” 2014. Thesis, University of Sydney. Accessed January 26, 2021. http://hdl.handle.net/2123/13539.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Brell, Courtney Gordon Gray. “Many-body models for topological quantum information .” 2014. Web. 26 Jan 2021.

Vancouver:

Brell CGG. Many-body models for topological quantum information . [Internet] [Thesis]. University of Sydney; 2014. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2123/13539.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Brell CGG. Many-body models for topological quantum information . [Thesis]. University of Sydney; 2014. Available from: http://hdl.handle.net/2123/13539

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

5. Noh, Jiho. Topological Photonics in 3D Photonic Structures.

Degree: 2020, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/18025jzn138

► Topological insulators are materials that have an insulating bulk but robust conducting states on their edges. These states are topologically protected in the sense that… (more)

Subjects/Keywords: Topological Photonics; Higher-Order Topological Insulators; Weyl Points

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APA (6^th Edition):

Noh, J. (2020). Topological Photonics in 3D Photonic Structures. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/18025jzn138

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Noh, Jiho. “Topological Photonics in 3D Photonic Structures.” 2020. Thesis, Penn State University. Accessed January 26, 2021. https://submit-etda.libraries.psu.edu/catalog/18025jzn138.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Noh, Jiho. “Topological Photonics in 3D Photonic Structures.” 2020. Web. 26 Jan 2021.

Vancouver:

Noh J. Topological Photonics in 3D Photonic Structures. [Internet] [Thesis]. Penn State University; 2020. [cited 2021 Jan 26]. Available from: https://submit-etda.libraries.psu.edu/catalog/18025jzn138.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Noh J. Topological Photonics in 3D Photonic Structures. [Thesis]. Penn State University; 2020. Available from: https://submit-etda.libraries.psu.edu/catalog/18025jzn138

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Michigan

6. Gu, Jiahua. Ground-state Overlaps and Topological Phase Transitions.

Degree: PhD, Physics, 2019, University of Michigan

URL: http://hdl.handle.net/2027.42/151491

► For decades, Landau’s theory of phase transition has provided a successful classification for quantum and classical states of matter based on their symmetry broken patterns,… (more)

▼ For decades, Landau’s theory of phase transition has provided a successful classification for quantum and classical states of matter based on their symmetry broken patterns, except for certain exotic quantum states such as the fractional quantum Hall (FQH) effect. However, such exotic phenomena are crucial for a complete understanding of the nature. This thesis explores new physical principles emerging from topology and topological states. First, we use an example to demonstrate Landau’s theory by studying a pair-density wave system, where the symmetry-breaking paradigm is applicable. It turns out that such a system exhibits the Kosterlitz-Thouless (KT) transition, a phase transition driven by the proliferation of topological defects, i.e. vortex-antivortex pairs. For topological systems, where symmetry broken pattern cannot be used as a classification tool, we prove a theorem that two gapped systems with non-vanishing ground-state overlap must be adiabatically connected, and thus are necessarily in the same topological phase. This theorem provides a simple and generic approach to classify topological band insulators/superconductors, without the needs to calculate any known or yet-to-known topological indices. Once the overlap is found nonzero, the two systems must be topologically identical. After presenting a generic proof, the theorem is also verified through calculating the overlap for several milestone topological band insulators and certain interacting systems. Such an overlap technique is then generalized to (2+1)-D strongly-interacting topological systems at fixed points, including both symmetry-protected topological (SPT) states and intrinsic topological states like FQH. For interacting topological states, the main challenge of utilizing wave-function overlaps to classify them lies in the famous Anderson orthogonality catastrophe (AOC), which states that two different many-body wave functions must have zero overlap in the thermodynamic limit. In this thesis, we found that wave-function overlaps indeed carry critical information about the topological nature of quantum states and this information can be extracted from the finite-size scaling of the overlaps. In the finite-size scaling analysis, we found a universal topological response term as a sub-leading contribution. This term depends on both the central charge of the corresponding conformal field theory (CFT) and the Euler characteristics of the underlying manifolds on which the system is defined. This term reveals a fundamental connection between ground-state overlaps and CFT’s. In addition, surprisingly, the overlap between an intrinsic topological state and a topologically trivial product state shows a decay faster than the exponential behavior expected via a typical AOC analysis. Such finite-size scaling behaviors could be utilized to theoretically detect the gapless edge modes, and to distinguish the topology of quantum states or serve as a signature of topological phase transitions. Possible generalization to higher dimensions and generic… Advisors/Committee Members: Sun, Kai (committee member), Kurdak, Cagliyan (committee member), Li, Lu (committee member), Liu, James T (committee member).

Subjects/Keywords: condensed matter; topological insulator; SPT; topological order; phase transition; quantum; Physics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gu, J. (2019). Ground-state Overlaps and Topological Phase Transitions. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/151491

Chicago Manual of Style (16^th Edition):

Gu, Jiahua. “Ground-state Overlaps and Topological Phase Transitions.” 2019. Doctoral Dissertation, University of Michigan. Accessed January 26, 2021. http://hdl.handle.net/2027.42/151491.

MLA Handbook (7^th Edition):

Gu, Jiahua. “Ground-state Overlaps and Topological Phase Transitions.” 2019. Web. 26 Jan 2021.

Vancouver:

Gu J. Ground-state Overlaps and Topological Phase Transitions. [Internet] [Doctoral dissertation]. University of Michigan; 2019. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2027.42/151491.

Council of Science Editors:

Gu J. Ground-state Overlaps and Topological Phase Transitions. [Doctoral Dissertation]. University of Michigan; 2019. Available from: http://hdl.handle.net/2027.42/151491

Penn State University

7. Liu, Qi. Quantum Engineering of Fractional Hall Physics in an Atom-Optical Laughlin-Pump Oscillator.

Degree: 2018, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/15726qxl125

► Quantum simulation in cold atomic physics has seen successes in many different fields and contexts of research. Simulation of gauge effects, often introduces new challenges,… (more)

Subjects/Keywords: Quantum Simulation; Topological Order; Laughlin's Quantum Pump; Driven Oscillator; Sagnac Interferometer

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APA (6^th Edition):

Liu, Q. (2018). Quantum Engineering of Fractional Hall Physics in an Atom-Optical Laughlin-Pump Oscillator. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/15726qxl125

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Liu, Qi. “Quantum Engineering of Fractional Hall Physics in an Atom-Optical Laughlin-Pump Oscillator.” 2018. Thesis, Penn State University. Accessed January 26, 2021. https://submit-etda.libraries.psu.edu/catalog/15726qxl125.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Liu, Qi. “Quantum Engineering of Fractional Hall Physics in an Atom-Optical Laughlin-Pump Oscillator.” 2018. Web. 26 Jan 2021.

Vancouver:

Liu Q. Quantum Engineering of Fractional Hall Physics in an Atom-Optical Laughlin-Pump Oscillator. [Internet] [Thesis]. Penn State University; 2018. [cited 2021 Jan 26]. Available from: https://submit-etda.libraries.psu.edu/catalog/15726qxl125.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Liu Q. Quantum Engineering of Fractional Hall Physics in an Atom-Optical Laughlin-Pump Oscillator. [Thesis]. Penn State University; 2018. Available from: https://submit-etda.libraries.psu.edu/catalog/15726qxl125

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

8. Moradi, Heidar. Topological Order and Universal Properties of Gapped Quantum Systems.

Degree: 2018, University of Waterloo

URL: http://hdl.handle.net/10012/14157

► Phases of gapped quantum liquids are topologically ordered and have very interesting physical features that are completely robust against any local perturbation that do not… (more)

Subjects/Keywords: topological order; condensed matter physics; mathematical physics; quantum physics

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APA (6^th Edition):

Moradi, H. (2018). Topological Order and Universal Properties of Gapped Quantum Systems. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/14157

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Moradi, Heidar. “Topological Order and Universal Properties of Gapped Quantum Systems.” 2018. Thesis, University of Waterloo. Accessed January 26, 2021. http://hdl.handle.net/10012/14157.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Moradi, Heidar. “Topological Order and Universal Properties of Gapped Quantum Systems.” 2018. Web. 26 Jan 2021.

Vancouver:

Moradi H. Topological Order and Universal Properties of Gapped Quantum Systems. [Internet] [Thesis]. University of Waterloo; 2018. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10012/14157.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Moradi H. Topological Order and Universal Properties of Gapped Quantum Systems. [Thesis]. University of Waterloo; 2018. Available from: http://hdl.handle.net/10012/14157

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Freie Universität Berlin

9. Wille, Carolin. Ein Tensornetzwerk-Zugang zu nicht-chiraler topologischer Ordnung.

Degree: 2020, Freie Universität Berlin

URL: http://dx.doi.org/10.17169/refubium-27277

► This Thesis discusses how non-chiral topological order in two-dimensions can be accessed within a tensor network framework. The approach is two-fold. On the one hand,… (more)

Subjects/Keywords: Quantum physics; Topological Order; Phases of Matter; ddc:539

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APA (6^th Edition):

Wille, C. (2020). Ein Tensornetzwerk-Zugang zu nicht-chiraler topologischer Ordnung. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-27277

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Wille, Carolin. “Ein Tensornetzwerk-Zugang zu nicht-chiraler topologischer Ordnung.” 2020. Thesis, Freie Universität Berlin. Accessed January 26, 2021. http://dx.doi.org/10.17169/refubium-27277.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Wille, Carolin. “Ein Tensornetzwerk-Zugang zu nicht-chiraler topologischer Ordnung.” 2020. Web. 26 Jan 2021.

Vancouver:

Wille C. Ein Tensornetzwerk-Zugang zu nicht-chiraler topologischer Ordnung. [Internet] [Thesis]. Freie Universität Berlin; 2020. [cited 2021 Jan 26]. Available from: http://dx.doi.org/10.17169/refubium-27277.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wille C. Ein Tensornetzwerk-Zugang zu nicht-chiraler topologischer Ordnung. [Thesis]. Freie Universität Berlin; 2020. Available from: http://dx.doi.org/10.17169/refubium-27277

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Colorado

10. Song, Hao. Interplay between Symmetry and Topological Order in Quantum Spin Systems.

Degree: PhD, Physics, 2015, University of Colorado

URL: https://scholar.colorado.edu/phys_gradetds/159

► In this thesis, we study the topological phases of quantum spin systems. One project is to investigate a class of anti-ferromagnetic SU(N) Heisenberg models,… (more)

Subjects/Keywords: Quantum spin liquid; SU(N) magnetism; Symmetry enriched topological order; Symmetry fractionalization; Symmetry protected topological order; Topological phase; Condensed Matter Physics; Quantum Physics

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APA (6^th Edition):

Song, H. (2015). Interplay between Symmetry and Topological Order in Quantum Spin Systems. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/phys_gradetds/159

Chicago Manual of Style (16^th Edition):

Song, Hao. “Interplay between Symmetry and Topological Order in Quantum Spin Systems.” 2015. Doctoral Dissertation, University of Colorado. Accessed January 26, 2021. https://scholar.colorado.edu/phys_gradetds/159.

MLA Handbook (7^th Edition):

Song, Hao. “Interplay between Symmetry and Topological Order in Quantum Spin Systems.” 2015. Web. 26 Jan 2021.

Vancouver:

Song H. Interplay between Symmetry and Topological Order in Quantum Spin Systems. [Internet] [Doctoral dissertation]. University of Colorado; 2015. [cited 2021 Jan 26]. Available from: https://scholar.colorado.edu/phys_gradetds/159.

Council of Science Editors:

Song H. Interplay between Symmetry and Topological Order in Quantum Spin Systems. [Doctoral Dissertation]. University of Colorado; 2015. Available from: https://scholar.colorado.edu/phys_gradetds/159

11. Jairo Rocha de Faria. Second order topological sensitivity analysis.

Degree: 2008, Laboratório Nacional de Computação Científica

URL: http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=141

►

The topological derivative provides the sensitivity of a given shape functional with respect to an infinitesimal non-smooth domain pertubation (insertion of hole or inclusion, for… (more)

▼

The topological derivative provides the sensitivity of a given shape functional with respect to an infinitesimal non-smooth domain pertubation (insertion of hole or inclusion, for instance). Classically, this derivative comes from the second term of the topological asymptotic expansion, dealing only with inifinitesimal pertubations. However, for pratical applications, we need to insert pertubations of finite sizes.Therefore, we consider other terms in the expansion, leading to the concept of higher-order topological derivatives. In a particular, we observe that the topological-shape sensitivity method can be naturally extended to calculate these new terms, resulting in a systematic methodology to obtain higher-order topological derivatives. In order to present these ideas, initially we apply this technique in some problems with exact solution, where the topological asymptotic expansion is obtained until third order. Later, we calculate first as well as second order topological derivative for the total potential energy associated to the Laplace equation in two-dimensional domain pertubed with the insertion of a hole, considering homogeneous Neumann or Dirichlet boundary conditions, or an inclusion with thermal conductivity coefficient value different from the bulk material. With these results, we present some numerical experiments showing the influence of the second order topological derivative in the topological asymptotic expansion, which has two main features:it allows us to deal with pertubations of finite sizes and provides a better descent direction in optimization and reconstruction algorithms.

A derivada topológica fornece a sensibilidade de uma dada função custo quando uma pertubação não suave e infinitesimal (furo ou inclusão, por exemplo) é introduzida. Classicamente, esta derivada vem do segundo termo da expansão assintótica topológica considerando-se apenas pertubações infinitesimais. No entanto, em aplicações práticas, é necessário considerar pertubação de tamanho finito. Motivado por este fato, o presente trabalho tem como objetivo fundamental introduzir o conceito de derivadas topológicas de ordem superiores, o que permite considerar mais termos na expansão assintótica topológica. Em particular, observa-se que o topological-shape sensitivity method pode ser naturalmente estendido para o cálculo destes novos termos, resultando em uma metodologia sistemática de análise de sensibilidade topológica de ordem superior. Para se apresentar essas idéias, inicialmente essa técnica é verificada através de alguns problemas que admitem solução exata, onde se calcula explicitamente a expansão assintótica topológica até terceira ordem. Posteriormente, considera-se a equação de Laplace bidimensional, cujo domínio é topologicamente pertubado pela introdução de um furo com condição de contorno de Neumann ou de Dirichlet homogêneas, ou ainda de uma inclusão com propriedade física distinta do meio. Nesse caso, são calculadas explicitamente as derivadas topológicas de primeira e segunda ordens. Com os resultados obtidos…

Advisors/Committee Members: Raul Antonino Feijóo, Abimael Fernando Dourado Loula, Jaime Edilberto Muñoz Rivera, Gustavo Alberto Perla Menzala, Antonio André Novotny, Edgardo Omar Taroco Aliano, Claudio Padra, Rodolfo Rodriguez, Fernando Pereira Duda, Walcy Santos.

Subjects/Keywords: EQUACOES DIFERENCIAIS PARCIAIS; Topological sensitivity analysis; Análise assintótica; Derivada topológica de segunda ordem; Derivada topológica; Análise de sensibilidade topológica; Topological rerivative; Second order topological derivative; Asymptotic analysis; EQUACOES DIFERENCIAIS PARCIAIS

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APA (6^th Edition):

Faria, J. R. d. (2008). Second order topological sensitivity analysis. (Doctoral Dissertation). Laboratório Nacional de Computação Científica. Retrieved from http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=141

Chicago Manual of Style (16^th Edition):

Faria, Jairo Rocha de. “Second order topological sensitivity analysis.” 2008. Doctoral Dissertation, Laboratório Nacional de Computação Científica. Accessed January 26, 2021. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=141.

MLA Handbook (7^th Edition):

Faria, Jairo Rocha de. “Second order topological sensitivity analysis.” 2008. Web. 26 Jan 2021.

Vancouver:

Faria JRd. Second order topological sensitivity analysis. [Internet] [Doctoral dissertation]. Laboratório Nacional de Computação Científica; 2008. [cited 2021 Jan 26]. Available from: http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=141.

Council of Science Editors:

Faria JRd. Second order topological sensitivity analysis. [Doctoral Dissertation]. Laboratório Nacional de Computação Científica; 2008. Available from: http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=141

Boston University

12. Iadecola, Thomas. Designing topological quantum matter in and out of equilibrium.

Degree: PhD, Physics, 2017, Boston University

URL: http://hdl.handle.net/2144/27071

► Recent advances in experimental condensed matter physics suggest a powerful new paradigm for the realization of exotic phases of quantum matter in the laboratory. Rather… (more)

▼ Recent advances in experimental condensed matter physics suggest a powerful new paradigm for the realization of exotic phases of quantum matter in the laboratory. Rather than conducting an exhaustive search for materials that realize these phases at low temperatures, it may be possible to design quantum systems that exhibit the desired properties. With the numerous advances made recently in the fields of cold atomic gases, superconducting qubits, trapped ions, and nitrogen-vacancy centers in diamond, it appears that we will soon have a host of platforms that can be used to put exotic theoretical predictions to the test. In this dissertation, I will highlight two ways in which theorists can interact productively with this fast-emerging field. First, there is a growing interest in driving quantum systems out of equilibrium in order to induce novel topological phases where they would otherwise never appear. In particular, systems driven by time-periodic perturbations—known as “Floquet systems”—offer fertile ground for theoretical investigation. This approach to designer quantum matter brings its own unique set of challenges. In particular, Floquet systems explicitly violate conservation of energy, providing no notion of a ground state. In the first part of my dissertation, I will present research that addresses this problem in two ways. First, I will present studies of open Floquet systems, where coupling to an external reservoir drives the system into a steady state at long times. Second, I will discuss examples of isolated quantum systems that exhibit signatures of topological properties in their finite-time dynamics. The second part of this dissertation presents another way in which theorists can benefit from the designer approach to quantum matter; in particular, one can design analytically tractable theories of exotic phases. I will present an exemplar of this philosophy in the form of coupled-wire constructions. In this approach, one builds a topological state of matter from the ground up by coupling together an array of one-dimensional quantum wires with local interactions. I will demonstrate the power of this technique by showing how to build both Abelian and non-Abelian topological phases in three dimensions by coupling together an array of quantum wires.

Subjects/Keywords: Condensed matter physics; Coupled-wire construction; Floquet theory; Non-Abelian topological phases; Periodically-driven quantum systems; Topological order; Topological states of matter

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APA (6^th Edition):

Iadecola, T. (2017). Designing topological quantum matter in and out of equilibrium. (Doctoral Dissertation). Boston University. Retrieved from http://hdl.handle.net/2144/27071

Chicago Manual of Style (16^th Edition):

Iadecola, Thomas. “Designing topological quantum matter in and out of equilibrium.” 2017. Doctoral Dissertation, Boston University. Accessed January 26, 2021. http://hdl.handle.net/2144/27071.

MLA Handbook (7^th Edition):

Iadecola, Thomas. “Designing topological quantum matter in and out of equilibrium.” 2017. Web. 26 Jan 2021.

Vancouver:

Iadecola T. Designing topological quantum matter in and out of equilibrium. [Internet] [Doctoral dissertation]. Boston University; 2017. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2144/27071.

Council of Science Editors:

Iadecola T. Designing topological quantum matter in and out of equilibrium. [Doctoral Dissertation]. Boston University; 2017. Available from: http://hdl.handle.net/2144/27071

University of California – Berkeley

13. Herdman, Christopher Mott. Loop Condensation in Quantum Dimer Models.

Degree: Physics, 2011, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/5nd482cr

► Topologically ordered phases of matter are quantum liquids with a non-local quantum order. Because of their unique properties due to the non-local quantum entanglement present… (more)

Subjects/Keywords: Condensed matter physics; Quantum physics; loop condensation; quantum dimer models; quantum Monte Carlo; topological order

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APA (6^th Edition):

Herdman, C. M. (2011). Loop Condensation in Quantum Dimer Models. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/5nd482cr

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Herdman, Christopher Mott. “Loop Condensation in Quantum Dimer Models.” 2011. Thesis, University of California – Berkeley. Accessed January 26, 2021. http://www.escholarship.org/uc/item/5nd482cr.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Herdman, Christopher Mott. “Loop Condensation in Quantum Dimer Models.” 2011. Web. 26 Jan 2021.

Vancouver:

Herdman CM. Loop Condensation in Quantum Dimer Models. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2021 Jan 26]. Available from: http://www.escholarship.org/uc/item/5nd482cr.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Herdman CM. Loop Condensation in Quantum Dimer Models. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/5nd482cr

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Cornell University

14. Sharma, Rahul. Advanced Quasiparticle Interference Imaging for Complex Superconductors.

Degree: PhD, Applied Physics, 2020, Cornell University

URL: http://hdl.handle.net/1813/70390

► State-of-the-art low-temperature spectroscopic imaging scanning tunneling microscopy offers a powerful tool to study materials with unprecedented spatial (subangstrom) and energy (micro-electronvolts) resolution. Imaging the quasiparticle… (more)

▼ State-of-the-art low-temperature spectroscopic imaging scanning tunneling microscopy offers a powerful tool to study materials with unprecedented spatial (subangstrom) and energy (micro-electronvolts) resolution. Imaging the quasiparticle interference of eigenstates in a material, offers a window into the underlying Hamiltonian. In this thesis, we performed quasiparticle interference imaging under extreme (milliKelvin temperatures) conditions and developed novel analysis techniques to address important contemporary problems in superconductivity which have defied complete understanding due to their complex multiband nature and small energy scales. Discovered almost 25 years ago, the momentum space gap structure of Sr2RuO4 has remained a mystery despite being an intensely researched topic due to possibilities of correlated and topological superconductivity. The multiband nature of Sr2RuO4 makes the problem complicated because usual thermodynamical probes cannot directly reveal which bands the subgap quasiparticles are coming from. Our first advanced approach addresses this problem by applying milliKelvin spectroscopic imaging scanning tunneling microscopy (SISTM) to visualize the Bogoliubov quasiparticle interference (BQPI) pattern deep within the superconducting gap at T=90 mK. From T-matrix modeling of the subgap scattering, we are able to conclude that the major gap lies on alpha:beta bands and the minima/nodes lie along (1; 1) directions. Further angular analysis of the scattering features reveals that the nodes must be within 0.05 radians of the (0; 0) - (1; 1) lines. These observations, along with the other theoretical and experimental literature at the present moment, are most consistent with a B1g symmetry (dx2-y2-wave) gap on alpha:beta bands of Sr2RuO4. This conclusion indicates that Sr2RuO4 may not be a chiral odd-parity superconductor as believed for many years. While many techniques exist to measure the magnitude of the superconducting gap, only a few can probe its phase. High-quality BQPI patterns can be analyzed for phase information to determine the sign of the gap. Such techniques rely on centering a single atomic defect in the field of view (FOV). Since the defect concentration determines the BQPI signal intensity, this usually forces the choice of a smaller field of view, limiting the momentum-space resolution and the BQPI signal intensity. As a second advanced approach, we implement quantum phase-sensitive technique which can work with multiple atomic defects in the FOV. We first show that our multiple atom phase-analysis technique reproduces the results for FeSe, a material previously studied with single impurity phase-analysis. Then we implement our technique to study LiFeAs. Our multi-atom analysis reveals that the gap sign changes from hole band to electron band. This establishes that the gap symmetry in LiFeAs is s. This multi-atom innovation extends applicability to more disordered superconductors, enables its application to larger fields of view thereby enhancing k-space resolution, and… Advisors/Committee Members: Muller, David (chair), Schlom, Darrell (committee member), Davis, James (committee member).

Subjects/Keywords: Condensed Matter Physics; Low Temperature Physics; Quasiparticle Interference; Superconducting Order Parameter; Superconductors; Topological Superconductors

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APA (6^th Edition):

Sharma, R. (2020). Advanced Quasiparticle Interference Imaging for Complex Superconductors. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/70390

Chicago Manual of Style (16^th Edition):

Sharma, Rahul. “Advanced Quasiparticle Interference Imaging for Complex Superconductors.” 2020. Doctoral Dissertation, Cornell University. Accessed January 26, 2021. http://hdl.handle.net/1813/70390.

MLA Handbook (7^th Edition):

Sharma, Rahul. “Advanced Quasiparticle Interference Imaging for Complex Superconductors.” 2020. Web. 26 Jan 2021.

Vancouver:

Sharma R. Advanced Quasiparticle Interference Imaging for Complex Superconductors. [Internet] [Doctoral dissertation]. Cornell University; 2020. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/1813/70390.

Council of Science Editors:

Sharma R. Advanced Quasiparticle Interference Imaging for Complex Superconductors. [Doctoral Dissertation]. Cornell University; 2020. Available from: http://hdl.handle.net/1813/70390

Boston College

15. Lu, Yuan-Ming. Exotic phases of correlated electrons in two dimensions.

Degree: PhD, Physics, 2011, Boston College

URL: http://dlib.bc.edu/islandora/object/bc-ir:101244

► Exotic phases and associated phase transitions in low dimensions have been a fascinating frontier and a driving force in modern condensed matter physics since the… (more)

▼ Exotic phases and associated phase transitions in low dimensions have been a fascinating frontier and a driving force in modern condensed matter physics since the 80s. Due to strong correlation effect, they are beyond the description of mean-field theory based on a single-particle picture and Landau's symmetry-breaking theory of phase transitions. These new phases of matter require new physical quantities to characterize them and new languages to describe them. This thesis is devoted to the study on exotic phases of correlated electrons in two spatial dimensions. We present the following efforts in understanding two-dimensional exotic phases: (1) Using Zn vertex algebra, we give a complete classification and characterization of different one-component fractional quantum Hall (FQH) states, including their ground state properties and quasiparticles. (2) In terms of a non-unitary transformation, we obtain the exact form of statistical interactions between composite fermions in the lowest Landau level (LLL) with v=1/(2m), m=1,2... By studying the pairing instability of composite fermions we theoretically explains recently observed FQHE in LLL with v=1/2,1/4. (3) We classify different Z2 spin liquids (SLs) on kagome lattice in Schwinger-fermion representation using projective symmetry group (PSG). We propose one most promising candidate for the numerically discovered SL state in nearest-neighbor Heisenberg model on kagome lattice}. (4) By analyzing different Z2 spin liquids on honeycomb lattice within PSG classification, we find out the nature of the gapped SL phase in honeycomb lattice Hubbard model, labeled sublattice pairing state (SPS) in Schwinger-fermion representation. We also identify the neighboring magnetic phase of SPS as a chiral-antiferromagnetic (CAF) phase and analyze the continuous phase transition between SPS and CAF phase. For the first time we identify a SL called 0-flux state in Schwinger-boson representation with one (SPS) in Schwinger-fermion representation by a duality transformation. (5) We show that when certain non-collinear magnetic order coexists in a singlet nodal superconductor, there will be Majorana bound states in vortex cores/on the edges of the superconductor. This proposal opens a window for discovering Majorana fermions in strongly correlated electrons. (6) Motivated by recent numerical discovery of fractionalized phases in topological flat bands, we construct wavefunctions for spin-polarized fractional Chern insulators (FCI) and time reversal symmetric fractional topological insulators (FTI) by parton approach. We show that lattice symmetries give rise to different FCI/FTI states even with the same filling fraction. For the first time we construct FTI wavefunctions in the absence of spin conservation which preserve all lattice symmetries. The constructed wavefunctions also set up the framework for future variational Monte Carlo simulations. Advisors/Committee Members: Ziqiang Wang (Thesis advisor).

Subjects/Keywords: fractional quantum Hall effect; Majorana fermion; spin liquid; strongly correlated electrons; topological order; vertex algebra

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APA (6^th Edition):

Lu, Y. (2011). Exotic phases of correlated electrons in two dimensions. (Doctoral Dissertation). Boston College. Retrieved from http://dlib.bc.edu/islandora/object/bc-ir:101244

Chicago Manual of Style (16^th Edition):

Lu, Yuan-Ming. “Exotic phases of correlated electrons in two dimensions.” 2011. Doctoral Dissertation, Boston College. Accessed January 26, 2021. http://dlib.bc.edu/islandora/object/bc-ir:101244.

MLA Handbook (7^th Edition):

Lu, Yuan-Ming. “Exotic phases of correlated electrons in two dimensions.” 2011. Web. 26 Jan 2021.

Vancouver:

Lu Y. Exotic phases of correlated electrons in two dimensions. [Internet] [Doctoral dissertation]. Boston College; 2011. [cited 2021 Jan 26]. Available from: http://dlib.bc.edu/islandora/object/bc-ir:101244.

Council of Science Editors:

Lu Y. Exotic phases of correlated electrons in two dimensions. [Doctoral Dissertation]. Boston College; 2011. Available from: http://dlib.bc.edu/islandora/object/bc-ir:101244

Princeton University

16. Guillen Pegueroles, Bernat. Smooth Selection Principles, Simplicial Complexes, and Everything in Between .

Degree: PhD, 2019, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01k643b405p

► This thesis is divided in three chapters, each of them completely self-contained, detailing the progress done in three projects. In the first chapter, we develop… (more)

Subjects/Keywords: Competition-Diffusion equations; Contagion Dynamics; High Order Dynamics; Non-convexity; Smooth Selection; Topological Data Analysis

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APA (6^th Edition):

Guillen Pegueroles, B. (2019). Smooth Selection Principles, Simplicial Complexes, and Everything in Between . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01k643b405p

Chicago Manual of Style (16^th Edition):

Guillen Pegueroles, Bernat. “Smooth Selection Principles, Simplicial Complexes, and Everything in Between .” 2019. Doctoral Dissertation, Princeton University. Accessed January 26, 2021. http://arks.princeton.edu/ark:/88435/dsp01k643b405p.

MLA Handbook (7^th Edition):

Guillen Pegueroles, Bernat. “Smooth Selection Principles, Simplicial Complexes, and Everything in Between .” 2019. Web. 26 Jan 2021.

Vancouver:

Guillen Pegueroles B. Smooth Selection Principles, Simplicial Complexes, and Everything in Between . [Internet] [Doctoral dissertation]. Princeton University; 2019. [cited 2021 Jan 26]. Available from: http://arks.princeton.edu/ark:/88435/dsp01k643b405p.

Council of Science Editors:

Guillen Pegueroles B. Smooth Selection Principles, Simplicial Complexes, and Everything in Between . [Doctoral Dissertation]. Princeton University; 2019. Available from: http://arks.princeton.edu/ark:/88435/dsp01k643b405p

University of New Mexico

17. Miller, Jacob E. Measurement-Based Quantum Computation and Symmetry-Protected Topological Order.

Degree: Physics & Astronomy, 2017, University of New Mexico

URL: https://digitalrepository.unm.edu/phyc_etds/149

► While quantum computers can achieve dramatic speedups over the classical computers familiar to us, identifying the origin of this quantum advantage in physical systems… (more)

▼ While quantum computers can achieve dramatic speedups over the classical computers familiar to us, identifying the origin of this quantum advantage in physical systems remains a major goal of quantum information science. A useful tool here is measurement-based quantum computation (MQC), a computational framework utilizing the quantum entanglement found in many-body resource states. Not all resource states are useful for quantum computation however, so an important question is what properties of many-body entanglement characterize universal resource states, which can implement any quantum computation. Many-body states are also studied in condensed matter physics, where the collective behavior of quantum many-body systems sometimes define topological phases of matter. These phases are defined by nonlocal many-body entanglement, making topologically-ordered states natural candidates for MQC. We might wonder if these topological phases could be organized as phases of quantum computation, so that every state within the phase is universal for MQC. While phases of symmetry-protected topological order (SPTO) have arisen as natural candidates, previous attempts to demonstrate an MQC-SPTO correspondence were mostly limited to nonuniversal 1D spin chains, leaving the important 2D setting wide open. In this dissertation, we explore the wide and varied connections between MQC and SPTO, and obtain new results for 1D and 2D systems. After identifying a new MQC-SPTO correspondence within 1D spin chains, we move up and explore the operational use of 2D states with two complementary forms of SPTO. We create a new Union Jack resource state, whose different form of SPTO than previous 2D resource states permits a hierarchical notion of MQC universality. This state leads us to consider an idealized model of 2D SPTO, where we show that an additional symmetry condition makes these model states form universal resources for MQC only when they have nontrivial SPTO. We finally study the intrinsic complexity of SPTO-inspired states for classically intractable sampling, and identify inherent advantages of MQC for this purpose. Our work highlights the rich complexity available in states of entangled quantum matter, providing new evidence which sharpens our understanding of the diverse connections between MQC and SPTO. Advisors/Committee Members: Akimasa Miyake, Carlton Caves, Ivan Deutsch, Andrew Landahl.

Subjects/Keywords: measurement-based quantum computation; MQC; MBQC; symmetry-protected topological order; SPTO; SPT; Physics; Quantum Physics

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APA (6^th Edition):

Miller, J. E. (2017). Measurement-Based Quantum Computation and Symmetry-Protected Topological Order. (Doctoral Dissertation). University of New Mexico. Retrieved from https://digitalrepository.unm.edu/phyc_etds/149

Chicago Manual of Style (16^th Edition):

Miller, Jacob E. “Measurement-Based Quantum Computation and Symmetry-Protected Topological Order.” 2017. Doctoral Dissertation, University of New Mexico. Accessed January 26, 2021. https://digitalrepository.unm.edu/phyc_etds/149.

MLA Handbook (7^th Edition):

Miller, Jacob E. “Measurement-Based Quantum Computation and Symmetry-Protected Topological Order.” 2017. Web. 26 Jan 2021.

Vancouver:

Miller JE. Measurement-Based Quantum Computation and Symmetry-Protected Topological Order. [Internet] [Doctoral dissertation]. University of New Mexico; 2017. [cited 2021 Jan 26]. Available from: https://digitalrepository.unm.edu/phyc_etds/149.

Council of Science Editors:

Miller JE. Measurement-Based Quantum Computation and Symmetry-Protected Topological Order. [Doctoral Dissertation]. University of New Mexico; 2017. Available from: https://digitalrepository.unm.edu/phyc_etds/149

University of Sydney

18. Williamson, Dominic. Symmetry-protected adiabatic quantum transistors .

Degree: 2014, University of Sydney

URL: http://hdl.handle.net/2123/13083

► The standard circuit model of quantum computation differs in principle from a modern day computer chip in that computation is brought to stationary qubits in… (more)

Subjects/Keywords: Quantum computation; Symmetry-protected topological order; Adiabatic quantum computation; Holonomic quantum computation

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APA (6^th Edition):

Williamson, D. (2014). Symmetry-protected adiabatic quantum transistors . (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/13083

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Williamson, Dominic. “Symmetry-protected adiabatic quantum transistors .” 2014. Thesis, University of Sydney. Accessed January 26, 2021. http://hdl.handle.net/2123/13083.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Williamson, Dominic. “Symmetry-protected adiabatic quantum transistors .” 2014. Web. 26 Jan 2021.

Vancouver:

Williamson D. Symmetry-protected adiabatic quantum transistors . [Internet] [Thesis]. University of Sydney; 2014. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2123/13083.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Williamson D. Symmetry-protected adiabatic quantum transistors . [Thesis]. University of Sydney; 2014. Available from: http://hdl.handle.net/2123/13083

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

19. Zhang, Yi. Theory of Topological Phenomena in Condensed Matter Systems.

Degree: Physics, 2012, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/8ss5q2td

► Topological phenomena in physical systems are determined by topological structures and are thus universal and protected against perturbations. We theoretically establish exotic topological phenomena and… (more)

▼ Topological phenomena in physical systems are determined by topological structures and are thus universal and protected against perturbations. We theoretically establish exotic topological phenomena and their consequences for experiments in crystalline systems such as topological insulators and topologically ordered phases. We show that protected one-dimensional fermionic modes may be associated with the line defects such as dislocations in three-dimensional topological insulators, and strong electron-electron repulsion may lead to topological Mott insulators via spontaneous spin-orbit correlations in three dimensions. We also predict anomalous Aharonov Bohm conductance oscillations maximized at half integer multiples of a flux quantum in a topological insulator nanowire with strong surface disorder, arising from surface curvature induced Berry phase. In addition, we classify three-dimensional inversion symmetric insulators and their quantized responses.Quantum entanglement provides a promising probe to the properties of many-body systems, especially topological phases not captured by local order parameters. We present a characterization of topological insulators using entanglement spectrum based only on bulk ground-state wave function. Further, by studying entanglement of trivial partitions, we establish topological order in candidate Gutzwiller projected wave functions for gapped spin liquids and Laughlin states; and with entanglement's dependence on the ground states for bipartition of a torus into two cylinders, we demonstrate a method to extract the modular matrices and statistics and braiding of quasiparticle excitations. Our method helps to determine the topological order with only the set of ground-state wave functions on a torus. Our variational Monte Carlo calculations of topological entanglement entropy agree well with theory. We also find a violation of the boundary law for a critical spin liquid of Gutzwiller projected Fermi sea on the triangular lattice, where the entanglement entropy's enhancement by a logarithmic factor reflects the presence of emergent fermions in a bosonic wave function.

Subjects/Keywords: Physics; Berry phase; topological defect; topological insulator; topological order; topological phenomena; variational Monte Carlo method

…topological order presents an explicit model that has a unified origin for gauge bosons and fermions… …commute in a non-Abelian topological order, providing a physical way to manipulate the encoded… …orders The topological order is motivated by the low energy effective theory of topological… …quantum entanglement. Examples of topological order include fractional quantum hall insulators… …x5D;. Typical hallmarks and characterizations of topological order include ground states…

10 more images…

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APA (6^th Edition):

Zhang, Y. (2012). Theory of Topological Phenomena in Condensed Matter Systems. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/8ss5q2td

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zhang, Yi. “Theory of Topological Phenomena in Condensed Matter Systems.” 2012. Thesis, University of California – Berkeley. Accessed January 26, 2021. http://www.escholarship.org/uc/item/8ss5q2td.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zhang, Yi. “Theory of Topological Phenomena in Condensed Matter Systems.” 2012. Web. 26 Jan 2021.

Vancouver:

Zhang Y. Theory of Topological Phenomena in Condensed Matter Systems. [Internet] [Thesis]. University of California – Berkeley; 2012. [cited 2021 Jan 26]. Available from: http://www.escholarship.org/uc/item/8ss5q2td.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhang Y. Theory of Topological Phenomena in Condensed Matter Systems. [Thesis]. University of California – Berkeley; 2012. Available from: http://www.escholarship.org/uc/item/8ss5q2td

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

20. HSU CHUANG-HAN. TOPOLOGICAL CRYSTALLINE INSULATORS: ELECTRONIC AND TRANSPORT PROPERTIES.

Degree: 2019, National University of Singapore

URL: https://scholarbank.nus.edu.sg/handle/10635/163168

Subjects/Keywords: topological crystalline insulator; symmetry-based indicator; nonlinear magnetotransport; higher order topological insulator

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

CHUANG-HAN, H. (2019). TOPOLOGICAL CRYSTALLINE INSULATORS: ELECTRONIC AND TRANSPORT PROPERTIES. (Thesis). National University of Singapore. Retrieved from https://scholarbank.nus.edu.sg/handle/10635/163168

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

CHUANG-HAN, HSU. “TOPOLOGICAL CRYSTALLINE INSULATORS: ELECTRONIC AND TRANSPORT PROPERTIES.” 2019. Thesis, National University of Singapore. Accessed January 26, 2021. https://scholarbank.nus.edu.sg/handle/10635/163168.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

CHUANG-HAN, HSU. “TOPOLOGICAL CRYSTALLINE INSULATORS: ELECTRONIC AND TRANSPORT PROPERTIES.” 2019. Web. 26 Jan 2021.

Vancouver:

CHUANG-HAN H. TOPOLOGICAL CRYSTALLINE INSULATORS: ELECTRONIC AND TRANSPORT PROPERTIES. [Internet] [Thesis]. National University of Singapore; 2019. [cited 2021 Jan 26]. Available from: https://scholarbank.nus.edu.sg/handle/10635/163168.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

CHUANG-HAN H. TOPOLOGICAL CRYSTALLINE INSULATORS: ELECTRONIC AND TRANSPORT PROPERTIES. [Thesis]. National University of Singapore; 2019. Available from: https://scholarbank.nus.edu.sg/handle/10635/163168

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

The Ohio State University

21. Shi, Bowen. Anyon theory in gapped many-body systems from entanglement.

Degree: PhD, Physics, 2020, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1587705058308889

► In this thesis, we present a theoretical framework that can derive a general anyon theory for 2D gapped phases from an assumption on the entanglement… (more)

Subjects/Keywords: Physics; Theoretical Physics; Quantum Physics; Anyons; quantum entanglement; topological entanglement entropy; quantum Markov state; entanglement area law; topological order; fusion rules; Verlinde formula

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APA (6^th Edition):

Shi, B. (2020). Anyon theory in gapped many-body systems from entanglement. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1587705058308889

Chicago Manual of Style (16^th Edition):

Shi, Bowen. “Anyon theory in gapped many-body systems from entanglement.” 2020. Doctoral Dissertation, The Ohio State University. Accessed January 26, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587705058308889.

MLA Handbook (7^th Edition):

Shi, Bowen. “Anyon theory in gapped many-body systems from entanglement.” 2020. Web. 26 Jan 2021.

Vancouver:

Shi B. Anyon theory in gapped many-body systems from entanglement. [Internet] [Doctoral dissertation]. The Ohio State University; 2020. [cited 2021 Jan 26]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1587705058308889.

Council of Science Editors:

Shi B. Anyon theory in gapped many-body systems from entanglement. [Doctoral Dissertation]. The Ohio State University; 2020. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1587705058308889

22. Sunny, Kuriakose A. Study on Fuzzy Ordered FuzzyTopological Spaces.

Degree: 1993, Cochin University of Science and Technology

URL: http://dyuthi.cusat.ac.in/purl/1602

► In this study we combine the notions of fuzzy order and fuzzy topology of Chang and define fuzzy ordered fuzzy topological space. Its various properties… (more)

Subjects/Keywords: Fuzzy Topological Spaces; Fuzzy Set Theory; Fuzzy Order

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APA (6^th Edition):

Sunny, K. A. (1993). Study on Fuzzy Ordered FuzzyTopological Spaces. (Thesis). Cochin University of Science and Technology. Retrieved from http://dyuthi.cusat.ac.in/purl/1602

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Sunny, Kuriakose A. “Study on Fuzzy Ordered FuzzyTopological Spaces.” 1993. Thesis, Cochin University of Science and Technology. Accessed January 26, 2021. http://dyuthi.cusat.ac.in/purl/1602.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sunny, Kuriakose A. “Study on Fuzzy Ordered FuzzyTopological Spaces.” 1993. Web. 26 Jan 2021.

Vancouver:

Sunny KA. Study on Fuzzy Ordered FuzzyTopological Spaces. [Internet] [Thesis]. Cochin University of Science and Technology; 1993. [cited 2021 Jan 26]. Available from: http://dyuthi.cusat.ac.in/purl/1602.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sunny KA. Study on Fuzzy Ordered FuzzyTopological Spaces. [Thesis]. Cochin University of Science and Technology; 1993. Available from: http://dyuthi.cusat.ac.in/purl/1602

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

23. Slagle, Kevin Jacob. Exotic, Topological, and Many Body Localized Quantum Phase Transitions.

Degree: 2016, University of California – eScholarship, University of California

URL: http://www.escholarship.org/uc/item/04t828xc

► In this thesis we will study recent examples of exotic, topological, and many body localized quantum phase transitions. In Chapter 2 we study the quantum… (more)

Subjects/Keywords: Condensed matter physics; exotic; many body localization; quantum phase transition; spin liquid; symmetry protected; topological order

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APA (6^th Edition):

Slagle, K. J. (2016). Exotic, Topological, and Many Body Localized Quantum Phase Transitions. (Thesis). University of California – eScholarship, University of California. Retrieved from http://www.escholarship.org/uc/item/04t828xc

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Slagle, Kevin Jacob. “Exotic, Topological, and Many Body Localized Quantum Phase Transitions.” 2016. Thesis, University of California – eScholarship, University of California. Accessed January 26, 2021. http://www.escholarship.org/uc/item/04t828xc.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Slagle, Kevin Jacob. “Exotic, Topological, and Many Body Localized Quantum Phase Transitions.” 2016. Web. 26 Jan 2021.

Vancouver:

Slagle KJ. Exotic, Topological, and Many Body Localized Quantum Phase Transitions. [Internet] [Thesis]. University of California – eScholarship, University of California; 2016. [cited 2021 Jan 26]. Available from: http://www.escholarship.org/uc/item/04t828xc.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Slagle KJ. Exotic, Topological, and Many Body Localized Quantum Phase Transitions. [Thesis]. University of California – eScholarship, University of California; 2016. Available from: http://www.escholarship.org/uc/item/04t828xc

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

24. Perreault, Brent. Identifying a Kitaev Spin Liquid.

Degree: PhD, Physics, 2016, University of Minnesota

URL: http://hdl.handle.net/11299/185143

► The search for quantum spin liquid (QSL) physics has been long and storied, but alpha-RuCl3 and the iridates A2IrO3 have opened up the possibility of… (more)

Subjects/Keywords: fractionalization; Kitaev; magnet; spin liquid; topological order

…states, such mutual statistics define what is known as a topological order for the phase. To… …signaled by the breaking of translation symmetry. Moreover, one can write down an order parameter… …see Fig. 1.2. This breaks spin-rotation symmetry and the corresponding order parameter is… …order. The characterization and identification of such system is the primary focus of this… …coupling between nearest-neighbor (NN) spins that favors spontaneous magnetic order…

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APA (6^th Edition):

Perreault, B. (2016). Identifying a Kitaev Spin Liquid. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/185143

Chicago Manual of Style (16^th Edition):

Perreault, Brent. “Identifying a Kitaev Spin Liquid.” 2016. Doctoral Dissertation, University of Minnesota. Accessed January 26, 2021. http://hdl.handle.net/11299/185143.

MLA Handbook (7^th Edition):

Perreault, Brent. “Identifying a Kitaev Spin Liquid.” 2016. Web. 26 Jan 2021.

Vancouver:

Perreault B. Identifying a Kitaev Spin Liquid. [Internet] [Doctoral dissertation]. University of Minnesota; 2016. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/11299/185143.

Council of Science Editors:

Perreault B. Identifying a Kitaev Spin Liquid. [Doctoral Dissertation]. University of Minnesota; 2016. Available from: http://hdl.handle.net/11299/185143

25. De Gottardi, Wade. Strong correlations and topological order in one-dimensional systems.

Degree: PhD, 0240, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34264

► This thesis presents theoretical studies of strongly correlated systems as well as topologically ordered systems in 1D. Non-Fermi liquid behavior characteristic of interacting 1D electron… (more)

▼ This thesis presents theoretical studies of strongly correlated systems as well as topologically ordered systems in 1D. Non-Fermi liquid behavior characteristic of interacting 1D electron systems is investigated with an emphasis on experimentally relevant setups and observables. The existence of end Majorana fermions in a 1D p-wave superconductor subject to periodic, incommensurate and disordered potentials is studied. The Tomonaga-Luttinger liquid (TLL), a model of interacting electrons in one spatial dimension, is considered in the context of two systems of experimental interest. First, a study of the electronic properties of single-walled armchair carbon nanotubes in the presence of transverse electric and magnetic fields is presented. As a result of their effect on the band structure and electron wave functions, fields alter the nature of the (effective) Coulomb interaction in tubes. In particular, it is found that fields couple to nanotube bands (or valleys), a quantum degree of freedom inherited from the underlying graphene lattice. As revealed by a detailed TLL calculation, it is predicted that fields induce electrons to disperse into their spin, band, and charge components. Fields also provide a means of tuning the shell-filling behavior associated with short tubes. The phenomenon of charge fractionalization is investigated in a one-dimensional ring. TLL theory predicts that momentum-resolved electrons injected into the ring will fractionalize into clockwise- and counterclockwise-moving quasiparticles. As a complement to transport measurements in quantum wires connected to leads, non-invasive measures involving the magnetic field profiles around the ring are proposed. Topological aspects of 1D p-wave superconductors are explored. The intimate connection between non-trivial topology (fermions) and spontaneous symmetry breaking (spins) in one-dimension is investigated. Building on this connection, a spin ladder system endowed with vortex degrees of freedom is proposed in order to study the effects that inhomogeneous potentials have on the topological phase diagram. Periodic vortex patterns yield a rich parameter space for tuning into a topologically non-trivial phase. This analysis hinges on the development of a topological invariant based on the wave function of Majorana fermions which inhabit the ends of the system and are robust to disorder. The method is generalized to aperiodic and disordered potentials. The topological phase diagram of such systems is studied; numerical and analytic results are found to be in close agreement. Advisors/Committee Members: Vishveshwara, Smitha (advisor), Mason, Nadya (Committee Chair), Vishveshwara, Smitha (committee member), Mestre, Jose P. (committee member), Stone, Michael (committee member).

Subjects/Keywords: Luttinger liquids; charge fractionalization; topological order

…fermionic systems and spin chains motivates us to consider how topological order is manifest in… …studies of topological superconducting order in 1D systems with a focus on connections to spin… …58 58 60 61 63 67 68 69 Chapter 6 Spin Chains, Topological Phases and Majorana Fermions… …7.3.2 Topological invariant . . . . . . . . . . . . . . . 7.3.3 Generalization of topological… …invariant . . . . . 7.3.4 Relation to Other Topological Invariants . . . . 7.4 Topology of various…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

De Gottardi, W. (2012). Strong correlations and topological order in one-dimensional systems. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34264

Chicago Manual of Style (16^th Edition):

De Gottardi, Wade. “Strong correlations and topological order in one-dimensional systems.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 26, 2021. http://hdl.handle.net/2142/34264.

MLA Handbook (7^th Edition):

De Gottardi, Wade. “Strong correlations and topological order in one-dimensional systems.” 2012. Web. 26 Jan 2021.

Vancouver:

De Gottardi W. Strong correlations and topological order in one-dimensional systems. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2142/34264.

Council of Science Editors:

De Gottardi W. Strong correlations and topological order in one-dimensional systems. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34264

University of Manchester

26. Nenov, Yavor Neychev. Computability of Euclidean spatial logics.

Degree: PhD, 2011, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/computability-of-euclidean-spatial-logics(d6bd9f01-660b-43f7-9320-419697997c8b).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.606867

► In the last two decades, qualitative spatial representation and reasoning, and in particular spatial logics, have been the subject of an increased interest from the… (more)

▼ In the last two decades, qualitative spatial representation and reasoning, and in particular spatial logics, have been the subject of an increased interest from the Artificial Intelligence community. By a spatial logic, we understand a formal language whose variables range over subsets of a fixed topological space, called regions, and whose non-logical primitives have fixed geometric meanings. A spatial logic for reasoning about regions in a Euclidean space is called a Euclidean spatial logic. We consider first-order and quantifier-free Euclidean spatial logics with primitives for topological relations and operations, the property of convexity and the ternary relation of being closer-than. We mainly focus on the computational properties of such logics, but we also obtain interesting model-theoretic results. We provide a systematic overview of the computational properties of firstorder Euclidean spatial logics and fill in some of the gaps left by the literature. We establish upper complexity bounds for the (undecidable) theories of logics based on Euclidean spaces of dimension greater than one, which yields tight complexity bounds for all but two of these theories. In contrast with these undecidability results, we show that the topological theories based on one-dimensional Euclidean space are decidable, but non-elementary. We also study the computational properties of quantifier-free Euclidean spatial logics, and in particular those able to express the property of connectedness. It is known that when variables range over regions in the Euclidean plane, one can find formulas in these languages satisfiable only by regions with infinitely many connected components. Using this result, we show that the corresponding logics are undecidable. Further, we show that there exist formulas that are satisfiable in higher-dimensional Euclidean space, but only by regions with infinitely many connected components. We finish by outlining how the insights gained from this result were used (by another author) to show the undecidability of certain quantifier-free Euclidean spatial logics in higher dimensions.

Subjects/Keywords: 006.3; spatial logics; qualitative spatial reasoning; computability; topological constraint languages; first-order logics; Euclidean spaces; region algebras

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APA (6^th Edition):

Nenov, Y. N. (2011). Computability of Euclidean spatial logics. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/computability-of-euclidean-spatial-logics(d6bd9f01-660b-43f7-9320-419697997c8b).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.606867

Chicago Manual of Style (16^th Edition):

Nenov, Yavor Neychev. “Computability of Euclidean spatial logics.” 2011. Doctoral Dissertation, University of Manchester. Accessed January 26, 2021. https://www.research.manchester.ac.uk/portal/en/theses/computability-of-euclidean-spatial-logics(d6bd9f01-660b-43f7-9320-419697997c8b).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.606867.

MLA Handbook (7^th Edition):

Nenov, Yavor Neychev. “Computability of Euclidean spatial logics.” 2011. Web. 26 Jan 2021.

Vancouver:

Nenov YN. Computability of Euclidean spatial logics. [Internet] [Doctoral dissertation]. University of Manchester; 2011. [cited 2021 Jan 26]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/computability-of-euclidean-spatial-logics(d6bd9f01-660b-43f7-9320-419697997c8b).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.606867.

Council of Science Editors:

Nenov YN. Computability of Euclidean spatial logics. [Doctoral Dissertation]. University of Manchester; 2011. Available from: https://www.research.manchester.ac.uk/portal/en/theses/computability-of-euclidean-spatial-logics(d6bd9f01-660b-43f7-9320-419697997c8b).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.606867

27. Benalcazar, Wladimir Alejandro. Electric multipole moments and higher-order topological phases in crystalline insulators and superconductors.

Degree: PhD, Physics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101538

► This dissertation discusses extensions of the theory of polarization in crystalline insulators. The notion that electronic wave functions of energy bands in crystalline insulators have… (more)

Subjects/Keywords: condensed matter physics; topological phases of matter; higher-order topological phases; topological insulators; topological superconductors; topological photonics; polarization; dipole moment; quadrupole moment; Majorana bound states

…and predict the existence of a higher-order topological insulator, which has insulating bulk… …phenomena and higher-order topological insulators with hinge-localized chiral modes associated… …Reflection eigenvalues of lower Wannier bands in the different topological classes of the Wannier… …Topological adiabatic pumping of electronic charge… …A weak topological insulator…

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APA (6^th Edition):

Benalcazar, W. A. (2018). Electric multipole moments and higher-order topological phases in crystalline insulators and superconductors. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101538

Chicago Manual of Style (16^th Edition):

Benalcazar, Wladimir Alejandro. “Electric multipole moments and higher-order topological phases in crystalline insulators and superconductors.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 26, 2021. http://hdl.handle.net/2142/101538.

MLA Handbook (7^th Edition):

Benalcazar, Wladimir Alejandro. “Electric multipole moments and higher-order topological phases in crystalline insulators and superconductors.” 2018. Web. 26 Jan 2021.

Vancouver:

Benalcazar WA. Electric multipole moments and higher-order topological phases in crystalline insulators and superconductors. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2142/101538.

Council of Science Editors:

Benalcazar WA. Electric multipole moments and higher-order topological phases in crystalline insulators and superconductors. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101538

28. Jimenez, Juan Pablo Ibieta. Campos de Gauge e matéria na rede - generalizando o Toric Code.

Degree: Mestrado, Física, 2015, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-16072015-144543/ ;

►

Fases topológicas da matéria são caracterizadas por terem uma degenerescên- cia do estado fundamental que depende da topologia da variedade em que o sistema físico… (more)

▼

Fases topológicas da matéria são caracterizadas por terem uma degenerescên- cia do estado fundamental que depende da topologia da variedade em que o sistema físico é definido, além disso apresentam estados excitados no interior do sistema que são interpretados como sendo quase-partículas com estatística de tipo anyonica. Estes sistemas apresentam também excitações sem gap de energia em sua borda. Fases topologicamente ordenadas distintas não podem ser distinguidas pelo esquema usual de quebra de simetria de Ginzburg-Landau. Nesta dissertação apresentamos como exemplo o modelo mais simples de um sistema com Ordem Topológica, a saber, o Toric Code (TC), introduzido originalmente por A. Kitaev em [1]. O estado fundamental deste modelo ap- resenta degenerescência igual a 4 quando incorporado à superfície de um toro. As excitações elementares são interpretadas como sendo quase-partículas com estatística do tipo anyonica. O TC é um caso especial de uma classe mais geral de models chamados de Quantum Double Models (QDMs), estes modelos podem ser entendidos como sendo uma implementação de Teorias de gauge na rede em (2 + 1) dimensões na formulação Hamiltoniana, em que os graus de liberdade vivem nas arestas da rede e são elementos do grupo de gauge G. Nós generalizamos estes modelos com a inclusão de campos de matéria nos vértices da rede. Também apresentamos uma construção detalhada de tais modelos e mostramos que eles são exatamente solúveis. Em particular, exploramos o modelo que corresponde à escolher o grupo de gauge como sendo o grupo cíclico Z2 e os graus de liberdade de matéria como sendo elementos de um espaço vetorial bidimensional V2. Além disso, mostramos que a degenerescência do estado fundamental não depende da topologia da variedade e obtemos os estados excitados mais elementares deste modelo.

Topological phases of matter are characterized for having a topologically dependent ground state degeneracy, anyonic quasi-particle bulk excitations and gapless edge excitations. Different topologically ordered phases of matter can not be distinguished by te usual Ginzburg-Landau scheme of symmetry breaking. Therefore, a new mathematical framework for the study of such phases is needed. In this dissertation we present the simplest example of a topologically ordered system, namely, the \\Toric Code (TC) introduced by A. Kitaev in [1]. Its ground state is 4-fold degenerate when embedded on the surface of a torus and its elementary excited states are interpreted as quasi-particle anyons. The TC is a particular case of a more general class of lattice models known as Quantum Double Models (QDMs) which can be interpreted as an implementation of (2+1) Lattice Gauge Theories in the Hamiltonian formulation with discrete gauge group G. We generalize these models by the inclusion of matter fields at the vertices of the lattice. We give a detailed construction of such models, we show they are exactly solvable and explore the case when the gauge group is set to be the abelian Z₂ cyclic group and the matter degrees of freedom to…

Advisors/Committee Members: Teotonio Sobrinho, Paulo.

Subjects/Keywords: Campos de matéria; Gauge Theory; Lattice Gauge Theory; Matter Fields; Ordem Topológica; Teorias de gauge; Teorias de gauge na rede; Topological Order

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APA (6^th Edition):

Jimenez, J. P. I. (2015). Campos de Gauge e matéria na rede - generalizando o Toric Code. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/43/43134/tde-16072015-144543/ ;

Chicago Manual of Style (16^th Edition):

Jimenez, Juan Pablo Ibieta. “Campos de Gauge e matéria na rede - generalizando o Toric Code.” 2015. Masters Thesis, University of São Paulo. Accessed January 26, 2021. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-16072015-144543/ ;.

MLA Handbook (7^th Edition):

Jimenez, Juan Pablo Ibieta. “Campos de Gauge e matéria na rede - generalizando o Toric Code.” 2015. Web. 26 Jan 2021.

Vancouver:

Jimenez JPI. Campos de Gauge e matéria na rede - generalizando o Toric Code. [Internet] [Masters thesis]. University of São Paulo; 2015. [cited 2021 Jan 26]. Available from: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-16072015-144543/ ;.

Council of Science Editors:

Jimenez JPI. Campos de Gauge e matéria na rede - generalizando o Toric Code. [Masters Thesis]. University of São Paulo; 2015. Available from: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-16072015-144543/ ;

29. CIFUENTES PARDO, JESUS DAVID. Understanding topological order in 1D fermion chains.

Degree: 2016, Universidad de los Andes

URL: https://documentodegrado.uniandes.edu.co/documentos/10003.pdf

► En esta tesis vamos a revisar el concepto de orden topol\'ogico, el cual ha sido de gran inter\'es durante los \'ultimos a\~nos . Este orden… (more)

Subjects/Keywords: Topological order; topology; Kitaev chain; edge state; Clifford algebra; symmetry.

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APA (6^th Edition):

CIFUENTES PARDO, J. D. (2016). Understanding topological order in 1D fermion chains. (Thesis). Universidad de los Andes. Retrieved from https://documentodegrado.uniandes.edu.co/documentos/10003.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

CIFUENTES PARDO, JESUS DAVID. “Understanding topological order in 1D fermion chains. ” 2016. Thesis, Universidad de los Andes. Accessed January 26, 2021. https://documentodegrado.uniandes.edu.co/documentos/10003.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

CIFUENTES PARDO, JESUS DAVID. “Understanding topological order in 1D fermion chains. ” 2016. Web. 26 Jan 2021.

Vancouver:

CIFUENTES PARDO JD. Understanding topological order in 1D fermion chains. [Internet] [Thesis]. Universidad de los Andes; 2016. [cited 2021 Jan 26]. Available from: https://documentodegrado.uniandes.edu.co/documentos/10003.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

CIFUENTES PARDO JD. Understanding topological order in 1D fermion chains. [Thesis]. Universidad de los Andes; 2016. Available from: https://documentodegrado.uniandes.edu.co/documentos/10003.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

30. XIONG TIANSHI. SECOND ORDER TOPOLOGICAL FEATURES IN FLOQUET SYSTEMS.

Degree: 2019, National University of Singapore

URL: https://scholarbank.nus.edu.sg/handle/10635/154981

Subjects/Keywords: topological insulators; high-order topology; corner mode; reflection symmetry; driven system; Floquet theory

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APA (6^th Edition):

TIANSHI, X. (2019). SECOND ORDER TOPOLOGICAL FEATURES IN FLOQUET SYSTEMS. (Thesis). National University of Singapore. Retrieved from https://scholarbank.nus.edu.sg/handle/10635/154981

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

TIANSHI, XIONG. “SECOND ORDER TOPOLOGICAL FEATURES IN FLOQUET SYSTEMS.” 2019. Thesis, National University of Singapore. Accessed January 26, 2021. https://scholarbank.nus.edu.sg/handle/10635/154981.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

TIANSHI, XIONG. “SECOND ORDER TOPOLOGICAL FEATURES IN FLOQUET SYSTEMS.” 2019. Web. 26 Jan 2021.

Vancouver:

TIANSHI X. SECOND ORDER TOPOLOGICAL FEATURES IN FLOQUET SYSTEMS. [Internet] [Thesis]. National University of Singapore; 2019. [cited 2021 Jan 26]. Available from: https://scholarbank.nus.edu.sg/handle/10635/154981.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

TIANSHI X. SECOND ORDER TOPOLOGICAL FEATURES IN FLOQUET SYSTEMS. [Thesis]. National University of Singapore; 2019. Available from: https://scholarbank.nus.edu.sg/handle/10635/154981

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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