One-particle density matrix of a trapped Lieb-Liniger anyonic gas

TL;DR

This paper characterizes the zero-temperature one-particle density matrix of trapped one-dimensional anyonic gases, providing exact asymptotic expansions and analyzing effects of trapping potentials using advanced field theory and Bethe Ansatz techniques.

Contribution

It introduces a novel method to derive exact asymptotic expansions of the one-particle density matrix for inhomogeneous anyonic gases, extending previous results to trapped systems.

Findings

Exact asymptotic expansion for homogeneous anyonic gases.

Analytic results for trapped gases with various potentials.

Differences between anyonic and bosonic gas correlations.

Abstract

We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the non-universal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansion of this correlation function, thus extending the available results in the Tonks-Girardeau limit. Next, we analyse trapped gases with non-trivial density profiles. By applying recent analytic and numerical techniques for inhomogeneous Luttinger liquids,we provide exact expansions for the one-particle density matrix. We present our results for different confining potentials, highlighting the main differences with respect to bosonic gases.