Instabilities in One-Dimensional Two-Component Atomic Fermi Gas with Two-Level Impurities

TL;DR

This paper investigates the stability of a one-dimensional two-component Fermi gas with two-level impurities, revealing mechanisms that lead to instabilities and the emergence of a new Fermi-liquid state at low energies.

Contribution

It introduces a detailed analysis of instability mechanisms in a Luttinger liquid with two-level impurities, highlighting the formation of a new Fermi-liquid ground state.

Findings

Identification of multiple non-Fermi-liquid excitations near the Fermi level

Discovery of an additional Fermi-liquid singularity due to many-particle scattering

Conditions for the Fermi-liquid state with a lower energy scale than the Kondo temperature

Abstract

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.