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arXiv:cond-mat/9305018 · Physical Review Letters

Spin-flavor separation and non-Fermi-liquid behavior in the multichannel Kondo problem: A large-Napproach

D. L. Cox, Andrei E. Ruckenstein

Published Sep 6, 1993• 112 citations
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Abstract

We present an analytical solution of a SU(N)\ifmmode\times\else\texttimes\fi{}SU(M) generalization of the multichannel single-impurity Kondo model in the limit N\ensuremath{\rightarrow}\ensuremath{\infty}, M\ensuremath{\rightarrow}\ensuremath{\infty}, with \ensuremath{\gamma}=M/N fixed. Non-Fermi-liquid behavior of the single electron Green function and of the local spin and flavor susceptibilities occurs in both regimes, N\ensuremath{\le}M and N>M, with leading critical exponents identical to those found in the conformal field theory solution for all N and M (with M\ensuremath{\ge}2). We explain this remarkable agreement and connect it to ``spin-flavor separation,'' the essential feature of the non-Fermi-liquid, fixed point.

DOI
10.1103/physrevlett.71.1613

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Exact 3D space- and time-dependent Green's functions are computed for the multichannel Kondo effect in the universal large-distance, long-time regime, using conformal field theory. They exhibit crossover from Fermi-liquid form far away, to singular non-Fermi-liquid behavior, near the impurity, where charge, spin, and ``flavor'' degrees of freedom become ``deconfined.'' Explicit expressions are given for the resistivity, \ensuremath{\rho}, for all k and for the spin-density and pair-density Green's functions, for k=2. For k=2, \ensuremath{\rho}(T)-\ensuremath{\rho}(0)\ensuremath{\propto}T1/2{\mathit{T}}^{1/2}T1/2 and the pair susceptibility \ensuremath{\propto}lnT.
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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.
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We discuss a multichannel SU(N) Kondo model which displays nontrivial zero-temperature phase transitions due to a conduction electron density of states vanishing with a power law at the Fermi level. In a particular large- N limit, the system is described by coupled integral equations corresponding to a dynamic saddle point. We exactly determine the universal low-energy behavior of spectral densities at the scale-invariant fixed points, obtain anomalous exponents, and compute scaling functions describing the crossover near the quantum-critical points. We argue that our findings are relevant to recent experiments on impurity-doped d-wave superconductors.