Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0408171 · Journal of the Physical Society of Japan

Kondo Problem and Related One-dimensional Quantum Systems: Bethe Ansatz Solution and Boundary Conformal Field Theory

Satoshi Fujimoto, Norio Kawakami

Published Jan 1, 2005• 3 citations
arXivHTMLPDF

Abstract

We review some exact results on Kondo impurity systems derived from Bethe-ansatz solutions and boundary conformal field theory with particular emphasis on universal aspects of the phenomenon. The finite-size spectra characterizing the low-energy fixed point are computed from the Bethe-ansatz solutions of various models related to the Kondo problem. Using the finite-size scaling argument, we investigate their exact critical properties. We also discuss that a universal relation between the Kondo effect and the impurity effect in one-dimensional quantum systems usefully expedites our understanding of these different phenomena.

DOI
10.1143/jpsj.74.67

Related papers

Exact Finite-Size Spectra in the Kondo Problem and Boundary Conformal Field Theory

Satoshi Fujimoto, N. Kawakami, Yang, S. -K.

The exact finite-size spectra for several quantum impurity models related to the Kondo problem are obtained from the Bethe ansatz solutions. Using the finite-size scaling in boundary conformal field theory, we determine various surface critical exponents from the exact spectrum, which accord with those obtained by Affleck and Ludwig with Kac-Moody fusion rules. Some applications to critical phenomena observed in connection with the orthogonality catastrophe are also discussed.

arXiv:cond-mat/9512059•Dec 8, 1995•0 citations

Microscopic calculations of the finite-size spectrum in the Kondo problem

Satoshi Fujimoto, Norio Kawakami, Sung-Kil Yang

The finite-size spectrum in the Kondo problem is obtained from the Bethe-ansatz solution of the exactly solved models. We investigate the Anderson model, the highly correlated SU(\ensuremath{\nu}) Anderson model, and the s-d exchange model. For all these models we find that the spectra exhibit the properties characteristic of the Fermi-liquid fixed point, and hence our microscopic calculations are in accordance with the results obtained by boundary conformal field theory with current algebra symmetry.

arXiv:cond-mat/9403039•Physical review. B, Condensed matter•Jul 1, 1994•19 citations

Kondo Problem and Related One-dimensional Quantum Systems : Bethe Ansatz Solution and Boundary Conformal Field Theory( Kondo Effect-40 Years after the Discovery)

Satoshi Fujimoto, Norio Kawakami

Journal of the Physical Society of Japan•Jan 15, 2005•0 citations

Role of open boundaries in the Bethe ansatz solution of the Kondo problem

Andrei A. Zvyagin

The Bethe ansatz solution for the Kondo problem with open boundary conditions is presented. We show that one of the features of the generic Kondo effect---the finite magnetic susceptibility at low energies (present in the Bethe ansatz solution for periodic boundary conditions for the same model)---is absent due to the effect of open edges, if one considers the total effect of the impurity and the open edge together. However, we show that the behavior of the dynamical magnetic impurity itself is similar for periodic and open boundaries. It is shown that a real static boundary local potential (magnetic field) cannot model all features of the behavior of the dynamical magnetic impurity in the generic Kondo situation.

Physical review. B, Condensed matter•Nov 18, 2002•2 citations

Exact Critical Exponents for Pseudo-Particles in the Kondo Problem

Satoshi Fujimoto, Norio Kawakami, S.-K. Yang

Exact critical exponents of the Green functions for pseudo-fermions and slave bosons in the SU($N$) Anderson model with $U\rightarrow\infty$ are obtained by using the Bethe ansatz solution and boundary conformal field theory. They are evaluated exactly for mixed valence systems and Kondo systems with crystalline fields. The results agree with the prediction of Menge and Müller-Hartmann, which coincide with those of the X-ray problem. Some implication of our results in one-dimensional chiral systems is also discussed.

arXiv:cond-mat/9507121•Journal of the Physical Society of Japan•Dec 15, 1995•10 citations

Kondo Effect in a Luttinger Liquid: Exact Results from Conformal Field Theory

Per Fröjdh, Henrik Johannesson

We report on exact results for the low-temperature thermodynamics of a spin- $\frac{1}{2}$ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.

arXiv:cond-mat/9505100•Physical Review Letters•Jul 10, 1995•97 citations
We review some exact results on Kondo impurity systems derived from Bethe-ansatz solutions and boundary conformal field theory with particular emphasis on universal aspects of the phenomenon. The finite-size spectra characterizing the low-energy fixed point are computed from the Bethe-ansatz solutions of various models related to the Kondo problem. Using the finite-size scaling argument, we investigate their exact critical properties. We also discuss that a universal relation between the Kondo effect and the impurity effect in one-dimensional quantum systems usefully expedites our understanding of these different phenomena.
The finite-size spectrum in the Kondo problem is obtained from the Bethe-ansatz solution of the exactly solved models. We investigate the Anderson model, the highly correlated SU(\ensuremath{\nu}) Anderson model, and the s-d exchange model. For all these models we find that the spectra exhibit the properties characteristic of the Fermi-liquid fixed point, and hence our microscopic calculations are in accordance with the results obtained by boundary conformal field theory with current algebra symmetry.
The Bethe ansatz solution for the Kondo problem with open boundary conditions is presented. We show that one of the features of the generic Kondo effect---the finite magnetic susceptibility at low energies (present in the Bethe ansatz solution for periodic boundary conditions for the same model)---is absent due to the effect of open edges, if one considers the total effect of the impurity and the open edge together. However, we show that the behavior of the dynamical magnetic impurity itself is similar for periodic and open boundaries. It is shown that a real static boundary local potential (magnetic field) cannot model all features of the behavior of the dynamical magnetic impurity in the generic Kondo situation.
Exact critical exponents of the Green functions for pseudo-fermions and slave bosons in the SU(NNN) Anderson model with U→∞U\rightarrow\inftyU→∞ are obtained by using the Bethe ansatz solution and boundary conformal field theory. They are evaluated exactly for mixed valence systems and Kondo systems with crystalline fields. The results agree with the prediction of Menge and Müller-Hartmann, which coincide with those of the X-ray problem. Some implication of our results in one-dimensional chiral systems is also discussed.
We report on exact results for the low-temperature thermodynamics of a spin- 12\frac{1}{2}21​ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.