Ground-state properties of hard-core anyons in one-dimensional optical lattices

TL;DR

This paper studies the ground-state properties of one-dimensional hard-core anyons in optical lattices, revealing how fractional statistics influence momentum distributions and orbital occupations, with results bridging Bose and Fermi limits.

Contribution

It provides an exact numerical analysis of how fractional statistics affect ground-state properties of anyons in 1D lattices, highlighting asymmetry and crossover behaviors.

Findings

Momentum distributions are symmetric at Bose and Fermi limits.

Asymmetry in momentum distribution arises from fractional statistics.

Occupation distributions show crossover from Bose to Fermi behavior.

Abstract

We investigate the ground-state properties of anyons confined in one-dimensional optical lattices with a weak harmonic trap using the exact numerical method based on Jordan-Wigner transformation. It is shown that in the Bose limit ($\chi =1$) and Fermi limit ($\chi=0$) the momentum distributions are symmetric but in between they are asymmetric. It turns out that the origin of asymmetry comes from the fractional statistics that anyons obey. The occupation distribution and the modulus of natural orbitals show crossover behaviours from the Bose limit to the Fermi limit.