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Acta Physica Sinica

FERMI AND NON-FERMI LIQUID BEHAVIOR OF THE MULTICHANNEL RESONANT-LEVEL MODEL

YUAN QING-SHAN, Chen Hong, Yumei Zhang, 同济大学波耳固体物理研究所

Published Jan 1, 1996• 0 citations
Publisher

Abstract

In this paper we have transformed the three-dimensional multichannel resonant-level model into one-dimensional model using ths s-wave scattering approximation, and then map it onto a single channel Kondo model at the operator level by use of a bosonization technique. The specific heat has been calculated and the Fermi and non-Fermi liquid behavior of the system have been discussed for two fixed point Hamiltonians.

DOI
10.7498/aps.45.1865

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In this paper we have transformed the three-dimensional multichannel resonant-level model into one-dimensional model using ths s-wave scattering approximation, and then map it onto a single channel Kondo model at the operator level by use of a bosonization technique. The specific heat has been calculated and the Fermi and non-Fermi liquid behavior of the system have been discussed for two fixed point Hamiltonians.
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.
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 NNN and f:f:f: for N< f,N<~f,N< f, the specific heat and the susceptibility are dominated by the NFL contributions; for N>fN>fN>f the leading contributions are Fermi-liquid-like, and the NFL behavior can be seen only to subleading order; and for N=fN=fN=f the behavior is marginal. We also analyze the possibility of physical realizations. We show by a detailed renormalization-group and 1/f1/f1/f analysis that the tunneling NNN-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.
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.