Resonance in One--Dimensional Fermi--Edge Singularity

TL;DR

This paper investigates the Fermi--edge singularity in a one-dimensional Tomonaga--Luttinger liquid, revealing new exponents for the singularity when considering backward scattering and electron-electron repulsion, and relating it to Kondo physics.

Contribution

It introduces a Coulomb gas approach to analyze backward scattering effects, deriving new exponents for the Fermi--edge singularity in 1D systems with repulsive interactions.

Findings

New exponent for Fermi--edge singularity with backward scattering

Infrared physics resembles Kondo problem

Electron-electron repulsion alters singularity behavior

Abstract

The problem of the Fermi--edge singularity in a one--dimensional Tomonaga--Luttinger liquid is reconsidered. The backward scattering of the conduction band electrons on the impurity--like hole in the valence band is analyzed by mapping the problem onto a Coulomb gas theory. For the case when the electron--electron interaction is repulsive the obtained exponent of the one--dimensional Fermi--edge singularity appears to be different from the exponent found in the previous studies. It is shown that the infrared physics of the Fermi--edge singularity in the presence of backward scattering and electron--electron repulsion resembles the physics of the Kondo problem.