Dynamic response of one-dimensional interacting fermions

TL;DR

This paper investigates how nonlinear dispersion and interactions in one-dimensional spinless fermions alter the dynamic structure factor, revealing universal features, broadening peaks, and power-law singularities dependent on interaction strength.

Contribution

It introduces a comprehensive analysis of the dynamic structure factor for nonlinear dispersing interacting fermions, highlighting new universal features and singularities.

Findings

Sharp peak broadens due to nonlinear dispersion and interactions

Structure factor becomes finite at large frequencies for fixed q

Spectral weight concentrates in a narrow frequency interval with power-law singularities

Abstract

We evaluate the dynamic structure factor $S(q,\omega)$ of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of $S(q,\omega)$. The sharp peak $S\propto q\delta(\omega-uq)$, characteristic for the Tomonaga-Luttinger model, broadens up; $S(q,\omega)$ for a fixed $q$ becomes finite at arbitrarily large $\omega$. The main spectral weight, however, is confined to a narrow frequency interval of the width $\delta\omega\sim q^2/m$. At the boundaries of this interval the structure factor exhibits power-law singularities with exponents depending on the interaction strength and on the wave number $q$.