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Journal of Experimental and Theoretical Physics

Transition in a Luttinger liquid with two-level impurities to the fermi-liquid state

L. A. Manakova

Published Jul 1, 2004• 0 citations
Publisher

Abstract

The mechanisms leading to instability of the non-Fermi-liquid state of a Luttinger liquid with two-level impurities are proposed. Since exchange scattering in 1D systems is two-channel scattering in a certain range of parameters, several types of non-Fermi-liquid excitations with different quantum numbers exist in the vicinity of the Fermi level. These excitations include, first, charge density fluctuations in the Luttinger liquid and, second, many-particle excitations due to two-channel exchange interaction, which are associated with band-type as well as impurity fermion states. It is shown that mutual scattering of many-particle excitations of various types leads to the emergence of an additional Fermi-liquid singularity in the vicinity of the Fermi level. The conditions under which the Fermi-liquid state with a new energy scale (which is much smaller than the Kondo temperature) is the ground state of the system are formulated.

DOI
10.1134/1.1787088

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•Jan 1, 1994•1 citation
The mechanisms leading to instability of the non-Fermi-liquid state of a Luttinger liquid with two-level impurities are proposed. Since exchange scattering in 1D systems is two-channel scattering in a certain range of parameters, several types of non-Fermi-liquid excitations with different quantum numbers exist in the vicinity of the Fermi level. These excitations include, first, charge density fluctuations in the Luttinger liquid and, second, many-particle excitations due to two-channel exchange interaction, which are associated with band-type as well as impurity fermion states. It is shown that mutual scattering of many-particle excitations of various types leads to the emergence of an additional Fermi-liquid singularity in the vicinity of the Fermi level. The conditions under which the Fermi-liquid state with a new energy scale (which is much smaller than the Kondo temperature) is the ground state of the system are formulated.
In the present paper one-dimensional two-component atomic Fermi gas is considered in long-wave limit as a Luttinger liquid. The mechanisms leading to instability of the non-Fermi-liquid state of a Luttinger liquid with two-level impurities are proposed. Since exchange scattering in 1D systems is two-channel scattering in a certain range of parameters, several types of non-Fermi-liquid excitations with different quantum numbers exist in the vicinity of the Fermi level. These excitations include, first, charge density fluctuations in the Luttinger liquid and, second, many-particle excitations due to two-channel exchange interaction, which are associated with band-type as well as impurity fermion states. It is shown that mutual scattering of many-particle excitations of various types leads to the emergence of an additional Fermi-liquid singularity in the vicinity of the Fermi level. The conditions under which the Fermi-liquid state with a new energy scale (which is much smaller than the Kondo temperature) is the ground state of the system are formulated.
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.
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.
We investigate the stability of conducting and insulating phases in multichannel Luttinger liquids with respect to embedding a single impurity. We devise a general approach for finding critical exponents of the conductance in the limits of both weak and strong scattering. In contrast to the one-channel Luttinger liquid, the system state in certain parametric regions depends on the scattering strength which results in the emergence of a bistability. Focusing on the two-channel liquid, the method developed here enables us to provide a generic analysis of phase boundaries governed by the most relevant (i.e., not necessarily single-particle) scattering mechanism. The present approach is applicable to channels of different nature as in fermion-boson mixtures, or to identical ones as on the opposite edges of a topological insulator. We show that interaction per se cannot provide protection in the particular case of topological insulators realized in narrow Hall bars.
The Kondo effect in a Luttinger liquid composed of right-moving, spin-up electrons and left-moving, spin-down electrons is mapped exactly onto the Kondo effect in a Fermi liquid. The transformation generates anisotropy in the exchange coupling, which explains the two most notable features of the Kondo effect in a full Luttinger liquid: the quenching of the impurity moment for ferromagnetic, as well as antiferromagnetic, exchange and a power-law dependence of the Kondo temperature on the exchange coupling. Impurity contributions to the low-energy thermodynamics have the same temperature dependence as in a Fermi liquid.
Non-Fermi liquid behavior is found for the first time in a two-dimensional (2D) system with non-singular interactions using Haldane’s bosonization scheme. The bosonized system is solved exactly by a generalized Bogoliubov transformation. The fermion momentum distribution, calculated using a generalized Mattis-Lieb technique, exhibits a non-universal power law in the vicinity of the Fermi surface for intermediate interaction strengths. In recent years, there has been great interest in possible non-Fermi-liquid-like behavior in the ground state of two-dimensional (2D) strongly correlated fermionic systems [1]. It is well-known that in one dimension the ground state of a fermionic system with arbitrarily weak interactions is not a Fermi liquid but a state usually known as a Luttinger liquid [2]. For the 2D case, many studies have suggested that, in the limit of weak interactions, this behavior does not appear [3]. Studies of systems with a small number of particles also suggest Fermi liquid behavior in 2D [4]. Although Khveshchenko et al have found non-Fermi-liquid behavior in 2D, they worked only with a singular long-range current-current interaction [5]. The one-dimensional Luttinger liquid solution can be obtained by a bosonization