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Physical Review B

Multichannel Anderson impurity behavior in a pure hybridization impurity model

Jianhui Dai

Published Dec 1, 2004• 1 citation
Publisher

Abstract

A single multichannel quantum impurity model with pure hybridizations between the localized and orbital degenerate conducting electrons is shown to exhibit several interesting impurity properties resembling that of the multichannel Anderson model. Particularly for two special kinds of hybridization parameters the model can be solved exactly by the Bethe ansatz method. In these integrable cases, the competition between the direct and exchange correlated hybridizations can produces either a Fermi-liquid or non-Fermi-liquid behavior at low temperatures.

DOI
10.1103/physrevb.70.212401

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A single multichannel quantum impurity model with pure hybridizations between the localized and orbital degenerate conducting electrons is shown to exhibit several interesting impurity properties resembling that of the multichannel Anderson model. Particularly for two special kinds of hybridization parameters the model can be solved exactly by the Bethe ansatz method. In these integrable cases, the competition between the direct and exchange correlated hybridizations can produces either a Fermi-liquid or non-Fermi-liquid behavior at low temperatures.
We study a one-dimensional n -channel highly correlated electron model (based on the supersymmetric t-J model) with a magnetic impurity of arbitrary spin S that can hybridize with up to one itinerant electron per channel. The model extends the multichannel Kondo problem to correlations in the host and to the mixed valence regime. The Bethe ansatz equations are derived and solved for the ground state and for low temperatures. We conclude that the critical non-Fermi-liquid (overscreened) behaviour cannot be reached for this interacting electron system. Possible applications of the model are discussed.
We present the solution of the $\mathrm{SU}(N)\ensuremath{\bigotimes}\mathrm{SU}(M)$ Anderson impurity model using the Bethe-Ansatz. We first explain what extensions to the formalism were required for the solution. Subsequently we determine the ground state and derive the thermodynamics over the full range of temperature and fields. We identify the different regimes of valence fluctuation at high temperatures, followed by moment formation or intrinsic mixed valence at intermediate temperatures and a low temperature non-Fermi liquid phase. Among other things we obtain the impurity entropy, charge valence, and specific heat over the full range of temperature. We show that the low-energy physics is governed by a line of fixed points. This describes non-Fermi-liquid behavior in the integral valence regime, associated with moment formation, as well as in the mixed valence regime where no moment forms.
We solve the two-channel Anderson impurity model using the Bethe-ansatz. We determine the ground state and derive the thermodynamics, obtaining the impurity entropy and specific heat over the full range of temperature. We show that the low-temperature physics is given by a line of fixed points describing a two-channel non-Fermi-liquid behavior in the integral valence regime associated with moment formation as well as in the mixed valence regime where no moment forms. We discuss the relevance for the theory of UBe13.
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.
We construct the boundary conformal field theory that describes the low-temperature behavior of the two-channel Anderson impurity model. The presence of an exactly marginal operator is shown to generate a line of stable fixed points parametrized by the charge valence nc{n}_{c}nc​ of the impurity. We calculate the exact zero-temperature entropy and impurity thermodynamics along the fixed line. We also derive the critical exponents of the characteristic Fermi edge singularities caused by time-dependent hybridization between conduction electrons and impurity. Our results suggest that in the mixed-valent regime ${(n}_{c}\ensuremath{\ne}0,1)$ the electrons participate in two competing processes, leading to frustrated screening of spin and channel degrees of freedom. By combining the boundary conformal field theory with the Bethe-Ansatz solution we obtain a complete description of the low-energy dynamics of the model.
Despite the fact that the low energy behavior of the basic Kondo model cannot be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres and others to have a simple "local Fermi liquid theory" description. That is, electronic degrees of freedom become effectively non-interacting in the zero energy limit. However, generalized versions of the Kondo model involving more than one channel or impurity may exhibit low energy behavior of a less trivial sort which can, nonetheless, be solved exactly using either Bethe ansatz or conformal field theory and bosonization techniques. Now the low energy limit exhibits interacting many body behavior. For example, processes in which a single electron scatters off the impurity into a multi electron-hole state have a non-vanishing (and sometimes large) amplitude at zero energy. This corresponds to a rare solveable example of non-Fermi liquid behavior. Essential features of these phenomena are reviewed.