Correlation Functions of One-Dimensional Lieb-Liniger Anyons

TL;DR

This paper analyzes the correlation functions of one-dimensional Lieb-Liniger anyons, providing new insights into their spectral properties and long-distance correlations at zero and finite temperatures.

Contribution

It clarifies the boundary conditions for anyonic fields and derives the asymptotics of correlation functions, extending previous results for quantum anyonic fluids.

Findings

Spectrum of low-lying excitations calculated

Asymptotic behavior of correlation functions derived

Extension of existing results to finite temperatures

Abstract

We have investigated the properties of a model of 1D anyons interacting through a $\delta$-function repulsive potential. The structure of the quasi-periodic boundary conditions for the anyonic field operators and the many-anyon wavefunctions is clarified. The spectrum of the low-lying excitations including the particle-hole excitations is calculated for periodic and twisted boundary conditions. Using the ideas of the conformal field theory we obtain the large-distance asymptotics of the density and field correlation function at the critical temperature T=0 and at small finite temperatures. Our expression for the field correlation function extends the results in the literature obtained for harmonic quantum anyonic fluids.