Ground-state properties of one-dimensional anyon gases

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 ($0\leq κ\leq π$). 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 $κ$ 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 $κ$ deviates from 0 (Bose statistics) and $π$ (Fermi statistics) for any coupling constant $c$. The momentum distribution evolves from a Bose distribution to a Fermi one as $κ$ varies from 0 to $π$. 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 $κ$. The peak at positive momentum will shift to negative momentum if $κ$ is negative.

6 pages, 5 figures, published version in Phys. Rev. A