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University of Southern California

1.
Tao, Yaqi.
Finite size effect and *Friedel* oscillations for a
*Friedel*-*Anderson* *impurity* by FAIR method.

Degree: PhD, Physics, 2012, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/112869/rec/2820

A compact solution consisting of 4-8 Slater states
(FAIR solution) is introduced to treat the Friedel Anderson and
Kondo impurity problem. The ground state energy is obtained with
impressively high accuracy. Net integrated polarization density is
calculated and it confirms the existence of Kondo cloud. ❧ Finite
size effect in the impurity problem is studied using FAIR method.
It is shown that the formation of a Kondo ground state requires a
minimum sample size and is accompanied by the presence of Kondo
cloud. ❧ The Friedel Oscillations in the vicinity of a
Friedel-Anderson impurity are investigated by FAIR method. The
development of Friedel oscillation with a phase shift of Pi/2
outside the Kondo radius is confirmed. And the amplitude of the
Friedel oscillations show a very similar behavior to that of a
simple non-interacting Friedel impurity with a narrow resonance at
the Fermi level. This similarity supports the concept of a ”Kondo”
resonance. And the Kondo resonance half width is suggested to be
E/2.4, where E¬is the Kondo energy calculated from
susceptibility.
*Advisors/Committee Members: Bergmann, Gerd (Committee Chair), Haas, Stephan W. (Committee Member), Thompson, Richard S. (Committee Member), Däppen, Werner (Committee Member), Dappen, Werner (Committee Member), Daeppen, Werner (Committee Member), Zhang, Jianfeng (Committee Member).*

Subjects/Keywords: Friedel oscillations; Friedel-Anderson impurity; FAIR; finite size; Kondo; Kondo cloud

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

APA (6^{th} Edition):

Tao, Y. (2012). Finite size effect and Friedel oscillations for a Friedel-Anderson impurity by FAIR method. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/112869/rec/2820

Chicago Manual of Style (16^{th} Edition):

Tao, Yaqi. “Finite size effect and Friedel oscillations for a Friedel-Anderson impurity by FAIR method.” 2012. Doctoral Dissertation, University of Southern California. Accessed April 24, 2019. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/112869/rec/2820.

MLA Handbook (7^{th} Edition):

Tao, Yaqi. “Finite size effect and Friedel oscillations for a Friedel-Anderson impurity by FAIR method.” 2012. Web. 24 Apr 2019.

Vancouver:

Tao Y. Finite size effect and Friedel oscillations for a Friedel-Anderson impurity by FAIR method. [Internet] [Doctoral dissertation]. University of Southern California; 2012. [cited 2019 Apr 24]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/112869/rec/2820.

Council of Science Editors:

Tao Y. Finite size effect and Friedel oscillations for a Friedel-Anderson impurity by FAIR method. [Doctoral Dissertation]. University of Southern California; 2012. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/112869/rec/2820

University of Southern California

2.
Zhang, Liye.
A compact numerical approximate solution for
*Friedel*-*Anderson* and Kondo problem.

Degree: PhD, Physics, 2010, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/350062/rec/107

A Friedel Artificially Inserted Resonance (FAIR) state
is introduced to approximate the ground state of the
Friedel-Anderson and Kondo problem. The ground state of the
Friedel-Anderson problem can be expressed by eight Slater states
and that of the Kondo problem can be expressed by four Slater
states. Each Slater state is composed of one d-electron or a FAIR
state, and n s-electrons that are orthogonal to the FAIR state.
From the rotation of the s-electrons basis in Hilbert space and the
optimization of those Slater states coefficients, the ground state
(singlet state) and the first excite state (triplet state) can be
obtained simultaneously. The excitation energy between the singlet
and the triplet state is treated as Kondo energy. The ground energy
from FAIR method of the Friedel-Anderson problem is far lower than
that from the Mean Field Theory solution. And the Kondo energy in
the Kondo problem is related to the coupling constant J by an
exponential factor.; The FAIR method is then extended from
1-channel to multi-channel problem. A compact approximate ground
state of the multi-channel Friedel-Anderson or Kondo problem is
constructed from the product of 1-channel ground state of all the
individual channels. The Parmenter’s Anderson model, which
considered the Coulomb interaction, Exchange interaction and
rotationally invariant in both the spin space and the real space,
is applied in the calculation. The FAIR solution shows much better
approximation to the ground state than the Mean Field approach
does. The FAIR method is also applied on the multi-channel Kondo
impurity problem. The multi-channel Kondo impurity ground state,
which satisfies the Hund’s Rule requirement, is constructed. From
the discussion of the magnetic anisotropy of the Kondo impurity,
the emergence of the Kondo resonance for large-spin atoms
(S>1/2) impurity is clearly related to the spin flip transition
process between delta Sz=1 degenerate Slater states. The sign and
magnitude of the magnetic anisotropy play essential roles in the
formation of the Kondo resonance.
*Advisors/Committee Members: Bergmann, Gerd (Committee Chair), Haas, Stephan (Committee Member), Nakano, Aiichiro (Committee Member), Dappen, Werner (Committee Member), Zhang, Jianfeng (Committee Member).*

Subjects/Keywords: Friedel-Anderson; Kondo problem; multi-channel Kondo impurity; Kondo energy; FAIR method; Friedel artificially inserted resonance method; mean field method; magnetic state; singlet state; triplet state; magnetic anisotropy

Record Details Similar Records

❌

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

APA (6^{th} Edition):

Zhang, L. (2010). A compact numerical approximate solution for Friedel-Anderson and Kondo problem. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/350062/rec/107

Chicago Manual of Style (16^{th} Edition):

Zhang, Liye. “A compact numerical approximate solution for Friedel-Anderson and Kondo problem.” 2010. Doctoral Dissertation, University of Southern California. Accessed April 24, 2019. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/350062/rec/107.

MLA Handbook (7^{th} Edition):

Zhang, Liye. “A compact numerical approximate solution for Friedel-Anderson and Kondo problem.” 2010. Web. 24 Apr 2019.

Vancouver:

Zhang L. A compact numerical approximate solution for Friedel-Anderson and Kondo problem. [Internet] [Doctoral dissertation]. University of Southern California; 2010. [cited 2019 Apr 24]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/350062/rec/107.

Council of Science Editors:

Zhang L. A compact numerical approximate solution for Friedel-Anderson and Kondo problem. [Doctoral Dissertation]. University of Southern California; 2010. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/350062/rec/107