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Physical review. B, Condensed matter

Kondo effect in a Luttinger liquid: A boundary-conformal-field-theory approach

P. Durganandini

Published Apr 1, 1996• 14 citations
Publisher

Abstract

The Kondo problem in a Luttinger liquid has been studied recently using a poor-man's-scaling method. Here, the problem is formulated using the recent boundary-conformal-field-theory technique, which allows us to describe the critical points exactly. We recover the results for the specific heat and susceptibility calculated for low temperatures.

DOI
10.1103/physrevb.53.r8832

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The Kondo problem in a Luttinger liquid has been studied recently using a poor-man's-scaling method. Here, the problem is formulated using the recent boundary-conformal-field-theory technique, which allows us to describe the critical points exactly. We recover the results for the specific heat and susceptibility calculated for low temperatures.
We report on exact results for the low-temperature thermodynamics of a spin- 12\frac{1}{2}21​ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.
The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.
We study the low-temperature properties of a spin-1/2 magnetic impurity coupled to a one-dimensional interacting electron system. Using a formalism by Affleck and Ludwig, with a scale invariant boundary condition replacing the impurity, we exploit boundary conformal field theory to deduce the impurity thermal and magnetic response. In the case of only forward electron scattering off the impurity, we predict the same critical scaling as for the two-channel Kondo effect for noninteracting electrons, but with a different Wilson ratio. Backward electron scattering off the impurity destabilizes this behavior and drives the system to a new fixed point. In the case of equal amplitudes for forward and backward scattering (Kondo interaction), we show that there are only two types of scaling behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a critical theory with an anomalous specific heat. The latter case agrees with a recent poor-man's scaling result proposed by Furusaki and Nagaosa. \textcopyright{} 1996 The American Physical Society.
We present results for the Kondo effect in two crossed Luttinger liquids by using boundary conformal field theory. We predict two types of critical behaviors: either a two-channel Kondo fixed point with a nonuniversal Wilson ratio or a theory with an anomalous reponse that is identical to that found by Furusaki and Nagaosa for the Kondo effect in a single Luttinger liquid. Moreover, we discuss the relevance of perturbations like channel anisotropy in restoring a Fermi-liquid-like Kondo fixed point, and compare our results with the Kondo effect in a two-band Hubbard system modeled by a channel-dependent Luttinger Hamiltonian. The suppression of backscattering off the impurity produces a model similar to the four-channel Kondo theory. Consequences are discussed.
The Kondo effect in a Luttinger liquid is studied using the renormalization group method. By renormalizing the boson fields, scaling equations to the second order for an arbitrary Luttinger interaction are obtained. For the ferromagnetic Kondo coupling, a spin bound state (triplet) can be realized without invoking a nearest neighbour spin interaction in agreement with the recent Bethe ansatz calculation. The scaling theory in the presence of the scalar potential shows that there is no interplay between the magnetic and non-magnetic interaction. Also a study on the crossover behaviour of the Kondo temperature between the exponential and the power-law type is presented.
A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-liquid behavior for strong electron-electron interactions, gc<12{g}_{c}<\frac{1}{2}gc​<21​, and anomalous power laws for 12<gc<1\frac{1}{2}<{g}_{c}<121​<gc​<1, where gc{g}_{c}gc​ is the correlation parameter of the Luttinger liquid. These findings resolve a recent controversy. If elastic potential scattering is present, we find a logarithmically divergent impurity susceptibility at gc<12{g}_{c}<\frac{1}{2}gc​<21​ that can be rationalized in terms of the two-channel Kondo model.