Response functions in multicomponent Luttinger liquids

TL;DR

This paper derives exact and approximate analytical expressions for the density-density correlation function in multicomponent Luttinger liquids, revealing power-like singularities and their exponents, with numerical illustrations for three components.

Contribution

It provides a novel analytic framework for understanding correlation functions in multicomponent Luttinger liquids with different velocities.

Findings

Exact integral expressions for correlation functions derived

Power-like singularities identified with computed exponents

Numerical results demonstrated for three-component systems

Abstract

We derive an analytic expression for the zero temperature Fourier transform of the density-density correlation function of a multicomponent Luttinger liquid with different velocities. By employing Schwinger identity and a generalized Feynman identity exact integral expressions are derived, and approximate analytical forms are given for frequencies close to each component singularity. We find power-like singularities and compute the corresponding exponents. Numerical results are shown for the case of three components.