arXiv:cond-mat/0105491 · Springer eBooks

Fermi and Non-Fermi Liquid Behavior of Quantum Impurity Models: A Diagrammatic Pseudo-Particle Approach

Johann Kroha, P. Wölfle

Published May 8, 2006• 1 citation

arXiv HTML PDF

DOI: 10.1007/0-387-21717-7_7

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arXiv:cond-mat/0105491 · Springer eBooks

Fermi and Non-Fermi Liquid Behavior of Quantum Impurity Models: A Diagrammatic Pseudo-Particle Approach

Johann Kroha, P. Wölfle

Published May 8, 2006• 1 citation

arXiv HTML PDF

DOI: 10.1007/0-387-21717-7_7

Related papers

Non-Fermi liquid behavior from dynamical effects of impurity scattering in correlated Fermi liquids

Vidhyadhiraja Sudhindra, Pramod Kumar

Bulletin of the American Physical SocietyMar 3, 20150 citations

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P. Schlottmann

Physica B Condensed MatterJul 1, 20000 citations

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Nuclear Physics BJul 1, 19997 citations

Solution of the multichannel Coqblin-Schrieffer impurity model and application to multilevel systems

Andrés Jerez, Natan Andrei, Gergely Zaránd

A complete Bethe ansatz solution of the $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(f)$ Coqblin-Schrieffer model and a detailed analysis of some physical applications of the model are given. As in the usual multichannel Kondo model, a variety of Fermi-liquid and non-Fermi-liquid (NFL) fixed points is found, whose nature depends on the impurity representation \ensuremath{\mu}. For $\ensuremath{\mu}=f,$ we find a Fermi-liquid fixed point, with the impurity spin completely screened. For $f>\ensuremath{\mu},$ the impurity is overscreened and the model has NFL properties. The form the NFL behavior takes depends on the $N$ and $f:$ for $N<~f,$ the specific heat and the susceptibility are dominated by the NFL contributions; for $N>f$ the leading contributions are Fermi-liquid-like, and the NFL behavior can be seen only to subleading order; and for $N=f$ the behavior is marginal. We also analyze the possibility of physical realizations. We show by a detailed renormalization-group and $1/f$ analysis that the tunneling $N$ -state problem can be mapped into the $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(f)$ exchange model, and discuss the subtle differences between the two models. As another physical realization we suggest a double quantum dot structure that can be described by means of an $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ model if the parameters of the dots are tuned appropriately.A complete Bethe ansatz solution of the $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(f)$ Coqblin-Schrieffer model and a detailed analysis of some physical applications of the model are given. As in the usual multichannel Kondo model, a variety of Fermi-liquid and non-Fermi-liquid (NFL) fixed points is found, whose nature depends on the impurity representation \ensuremath{\mu}. For $\ensuremath{\mu}=f,$ we find a Fermi-liquid fixed point, with the impurity spin completely screened. For $f>\ensuremath{\mu},$ the impurity is overscreened and the model has NFL properties. The form the NFL behavior takes depends on the $N$ and $f:$ for $N<~f,$ the specific heat and the susceptibility are dominated by the NFL contributions; for $N>f$ the leading contributions are Fermi-liquid-like, and the NFL behavior can be seen only to subleading order; and for $N=f$ the behavior is marginal. We also analyze the possibility of physical realizations. We show by a detailed renormalization-group and $1/f$ analysis that the tunneling $N$-state problem can be mapped into the $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(f)$ exchange model, and discuss the subtle differences between the two models. As another physical realization we suggest a double quantum dot structure that can be described by means of an $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ model if the parameters of the dots are tuned appropriately.

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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.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.

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N

and

f:

for

N<~f,

the specific heat and the susceptibility are dominated by the NFL contributions; for

N>f

the leading contributions are Fermi-liquid-like, and the NFL behavior can be seen only to subleading order; and for

N=f

the behavior is marginal. We also analyze the possibility of physical realizations. We show by a detailed renormalization-group and

1/f

analysis that the tunneling

N

-state problem can be mapped into the $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(f)$ exchange model, and discuss the subtle differences between the two models. As another physical realization we suggest a double quantum dot structure that can be described by means of an $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ model if the parameters of the dots are tuned appropriately.

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.