Ground state properties of hard-core anyons in a harmonic potential

TL;DR

This paper analyzes the ground state properties of one-dimensional hard-core anyons in a harmonic trap, deriving analytical formulas and exploring how their properties interpolate between bosons and fermions.

Contribution

It provides a new analytical approach to study hard-core anyons in a harmonic potential, revealing their continuous transition between bosonic and fermionic behaviors.

Findings

Derived analytical formula for the reduced one-body density matrix.

Evaluated momentum distribution and natural orbitals for various statistical parameters.

Showed that larger statistical parameters lead to properties similar to hard-core bosons.

Abstract

Using anyon-fermion mapping method, we investigate the ground state properties of hard-core anyons confined in a one-dimensional harmonic trap. The concise analytical formula of the reduced one-body density matrix are obtained. Basing on the formula, we evaluated the momentum distribution, the natural orbitals and their occupation distributions for different statistical parameters. The occupation and occupation fraction of the lowest natural orbital versus anyon number are also displayed. It is shown that the ground state properties of anyons interplay between Bosons and Fermions continuously. We can expect that the hard-core anyons of larger statistical parameter exhibit the similar properties to the hard-core Bosons although anyon system satisfy specific fractional statistics.