Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices

TL;DR

This paper develops a method to compute correlation functions and momentum distributions of one-dimensional hard-core anyons in optical lattices, providing insights into their fractional statistics and thermal behavior.

Contribution

It introduces Fredholm determinant representations for Green's functions of hard-core anyons, enabling detailed numerical analysis of their correlations and momentum distributions.

Findings

Derived large-distance asymptotics of correlators

Computed momentum distribution at various temperatures

Numerical results reveal features of fractional statistics

Abstract

We address the problem of calculating the correlation functions in a system of one-dimensional hard-core anyons that can be experimentally realized in optical lattices. Using the summation of form factors we have obtained Fredholm determinant representations for the time-, space-, and temperature-dependent Green's functions which are particularly suited to numerical investigations. In the static case we have also derived the large distance asymptotic behavior of the correlators and computed the momentum distribution function at zero and finite temperature. We present extensive numerical results highlighting the characteristic features of one-dimensional systems with fractional statistics.