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

Physical Review Letters

Crossover from Non-Fermi-Liquid to Fermi-Liquid Behavior in the Two Channel Kondo Model with Channel Anisotropy

Michele Fabrizio, Alexander O. Gogolin, Ph. Nozières

Published May 29, 1995• 71 citations
Publisher

Abstract

We present a solution of the two channel Kondo model with channel anisotropic exchange couplings. The solution provides an analytic description of the crossover from a high temperature regime, dominated by the non-Fermi-liquid behavior of the isotropic two channel Kondo model, to a low temperature regime characterized by the standard Fermi-liquid behavior of the single channel Kondo model.

DOI
10.1103/physrevlett.74.4503

Related papers

Crossover Temperature from Non-Fermi Liquid to Fermi Liquid Behavior in Two Types of Impurity Kondo Model

Satoshi Yotsuhashi, Hideaki Maebashi

Numerical renormalization-group results on entropy of the anisotropic two-channel Kondo model with the band-width cutoff ($D$) in the presence of a magnetic field ($h$) are obtained to determine crossover temperature from the non-Fermi liquid to Fermi liquid fixed point. It is found that the crossover temperature ($T_{\rm x}$) is given by $T_{\rm x} \equiv {r} T_{\rm K} \sim D(ΔJ/J_{\rm av})^2 e^{-1/J_{\rm av}}$ when $(h /T_{\rm K})^2 \ll r \ll 1 $, where $T_{\rm K}$, $J_{\rm av}$ and $ΔJ$ are the Kondo temperature, the average and difference of the exchange coupling constants, respectively. This result indicates that non-Fermi liquid behavior can be seen even if $ΔJ > T_{\rm K}$. Robust similarities of the crossover behavior in the region around the non-Fermi liquid critical point to that of the two-impurity Kondo model are also discussed.

arXiv:cond-mat/0203506•Journal of the Physical Society of Japan•Jul 15, 2002•12 citations

Instability of Non-Fermi Liquid Behavior in the Two-Channel Kondo Model

Yuan Qing-Shan, Chen Hong, Yumei Zhang

The effects of interchannel scattering of conduction electrons by the impurity and repulsion of conduction electrons at the impurity site on the two-channel Kondo model are simultaneously considered in this paper. It is shown that these two perturbations will substantially modify the usual local non-Fermi liquid behavior of the two-channel Kondo model. With bosonization and unitary transformations we find that the system can be transformed into a single channel Kondo model with anisotropy between longitudinal and transverse exchange couplings. Whatever for originally antiferromagnetic or ferromagnetic isotropic coupling, the system always flows to strong-coupling limit, which exhibits local Fermi liquid behavior at low temperatures.

Communications in Theoretical Physics•May 15, 2001•0 citations

Anderson-Yuval approach to the multichannel Kondo problem

Michele Fabrizio, Alexander O. Gogolin, Ph. Nozières

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant-level model. Limiting cases in which the equivalent resonant-level model is solvable are identified. The solution correctly captures the properties of the two-channel Kondo model, and also allows an analytic description of the crossover from the non-Fermi-liquid to the Fermi-liquid behavior caused by the channel anisotropy.

arXiv:cond-mat/9412118•Physical review. B, Condensed matter•Jun 1, 1995•51 citations

Fermi- and Non-Fermi-Liquid Behavior in the Anisotropic Multichannel Kondo Model: Bethe Ansatz Solution

Natan Andrei, Andrés Jerez

We solve the multichannel Kondo model with channel anisotropy using the Bethe ansatz method. The model generates energy scales, characterizing the neighborhoods of the various infrared fixed points, reflecting the structure of the symmetry breaking in the channel sector. The nature of these fixed points also depends on the magnitude of the impurity spin $S$. We present a detailed discussion for the two channel case and point out some possible non-Fermi-liquid behavior.

arXiv:cond-mat/9412054•Physical Review Letters•May 29, 1995•95 citations

Universal low-temperature crossover in two-channel Kondo models

Andrew K. Mitchell, Eran Sela

An exact expression is derived for the electron Green function in two-channel Kondo models with one and two impurities, describing the crossover from non-Fermi liquid (NFL) behavior at intermediate temperatures to standard Fermi liquid (FL) physics at low temperatures. Symmetry-breaking perturbations generically present in experiment ensure the standard low-energy FL description, but the full crossover is wholly characteristic of the unstable NFL state. Distinctive conductance lineshapes in quantum dot devices should result. We exploit a connection between this crossover and one occurring in a classical boundary Ising model to calculate real-space electron densities at finite temperature. The single universal finite-temperature Green function is then extracted by inverting the integral transformation relating these Friedel oscillations to the $t$ matrix. Excellent agreement is demonstrated between exact results and full numerical renormalization group calculations.

arXiv:1203.4456•Physical Review B•Jun 18, 2012•61 citations

Exact Crossover Green Function in the Two-Channel and Two-Impurity Kondo Models

Eran Sela, Andrew K. Mitchell, Lars Fritz

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.

arXiv:1101.3028•Physical Review Letters•Apr 5, 2011•55 citations
We present a solution of the two channel Kondo model with channel anisotropic exchange couplings. The solution provides an analytic description of the crossover from a high temperature regime, dominated by the non-Fermi-liquid behavior of the isotropic two channel Kondo model, to a low temperature regime characterized by the standard Fermi-liquid behavior of the single channel Kondo model.
Numerical renormalization-group results on entropy of the anisotropic two-channel Kondo model with the band-width cutoff (DDD) in the presence of a magnetic field (hhh) are obtained to determine crossover temperature from the non-Fermi liquid to Fermi liquid fixed point. It is found that the crossover temperature (TxT_{\rm x}Tx​) is given by Tx≡rTK∼D(ΔJ/Jav)2e−1/JavT_{\rm x} \equiv {r} T_{\rm K} \sim D(ΔJ/J_{\rm av})^2 e^{-1/J_{\rm av}}Tx​≡rTK​∼D(ΔJ/Jav​)2e−1/Jav​ when $(h /T_{\rm K})^2 \ll r \ll 1 $, where TKT_{\rm K}TK​, JavJ_{\rm av}Jav​ and ΔJΔJΔJ are the Kondo temperature, the average and difference of the exchange coupling constants, respectively. This result indicates that non-Fermi liquid behavior can be seen even if ΔJ>TKΔJ > T_{\rm K}ΔJ>TK​. Robust similarities of the crossover behavior in the region around the non-Fermi liquid critical point to that of the two-impurity Kondo model are also discussed.
The effects of interchannel scattering of conduction electrons by the impurity and repulsion of conduction electrons at the impurity site on the two-channel Kondo model are simultaneously considered in this paper. It is shown that these two perturbations will substantially modify the usual local non-Fermi liquid behavior of the two-channel Kondo model. With bosonization and unitary transformations we find that the system can be transformed into a single channel Kondo model with anisotropy between longitudinal and transverse exchange couplings. Whatever for originally antiferromagnetic or ferromagnetic isotropic coupling, the system always flows to strong-coupling limit, which exhibits local Fermi liquid behavior at low temperatures.
We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant-level model. Limiting cases in which the equivalent resonant-level model is solvable are identified. The solution correctly captures the properties of the two-channel Kondo model, and also allows an analytic description of the crossover from the non-Fermi-liquid to the Fermi-liquid behavior caused by the channel anisotropy.
We solve the multichannel Kondo model with channel anisotropy using the Bethe ansatz method. The model generates energy scales, characterizing the neighborhoods of the various infrared fixed points, reflecting the structure of the symmetry breaking in the channel sector. The nature of these fixed points also depends on the magnitude of the impurity spin SSS. We present a detailed discussion for the two channel case and point out some possible non-Fermi-liquid behavior.
An exact expression is derived for the electron Green function in two-channel Kondo models with one and two impurities, describing the crossover from non-Fermi liquid (NFL) behavior at intermediate temperatures to standard Fermi liquid (FL) physics at low temperatures. Symmetry-breaking perturbations generically present in experiment ensure the standard low-energy FL description, but the full crossover is wholly characteristic of the unstable NFL state. Distinctive conductance lineshapes in quantum dot devices should result. We exploit a connection between this crossover and one occurring in a classical boundary Ising model to calculate real-space electron densities at finite temperature. The single universal finite-temperature Green function is then extracted by inverting the integral transformation relating these Friedel oscillations to the ttt matrix. Excellent agreement is demonstrated between exact results and full numerical renormalization group calculations.
Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.