Ground-state properties of one-dimensional anyon gases

TL;DR

This paper analyzes the ground state of one-dimensional anyon gases using Bethe ansatz, revealing how the statistics parameter influences momentum distribution and energy, bridging Bose and Fermi behaviors.

Contribution

It provides an exact solution for the ground state properties of 1D anyon gases across all coupling and statistics parameters, highlighting the impact on momentum distribution.

Findings

Momentum distribution transitions from Bose to Fermi as  varies from 0 to 

Anyonic statistics induce asymmetric momentum distribution when  deviates from 0 or 

Peak shifts in momentum distribution depend on the sign of 

Abstract

We investigate the ground state of the one-dimensional interacting anyonic system based on the exact Bethe ansatz solution for arbitrary coupling constant ($0\leq c\leq \infty$) and statistics parameter ($0\leq \kappa \leq \pi$). It is shown that the density of state in quasi-momentum $k$ space and the ground state energy are determined by the renormalized coupling constant $c'$. The effect induced by the statistics parameter $\kappa$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $\kappa$ deviates from 0 (Bose statistics) and $\pi$ (Fermi statistics) for any coupling constant $c$. The momentum distribution evolves from a Bose distribution to a Fermi one as $\kappa$ varies from 0 to $\pi$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the non-diagonal element of reduced density matrix, which is an odd function of $\kappa$. The peak at positive momentum will shift to negative momentum if $\kappa$ is negative.