Fermi-Edge Singularity with Backscattering in the Luttinger-Liquid Model

TL;DR

This paper investigates how backscattering influences the Fermi-edge singularity in a one-dimensional Luttinger liquid, revealing universal critical behavior dependent solely on interaction parameters.

Contribution

It provides a theoretical analysis of backscattering effects on Fermi-edge singularities, highlighting a universal critical exponent in the Luttinger-liquid model.

Findings

Backscattering modifies power-law singularities at low frequencies.

The critical exponent depends only on Luttinger-liquid interactions.

Results are applicable to 1D boson chain responses.

Abstract

We study the response of the interacting electron gas in one dimension on the local external potential. In the low frequency limit the power-law singularities are essentially modifyed by backscattering effects which, in the case of zero forward scattering, result in the universal critical exponent depending only on the Luttinger-liquid interactions. The results obtained may be used to describe singular responses of the 1D boson chains.