One-dimensional hard-core anyon gas in a harmonic trap at finite temperature

TL;DR

This paper studies the finite-temperature properties of one-dimensional hard-core anyon gases in a harmonic trap, revealing how their statistical behavior interpolates between Bose and Fermi gases and providing new insights into their momentum distribution and Tan's contact.

Contribution

The paper introduces a thermal anyon-fermion mapping method to analyze finite-temperature properties of hard-core anyon gases, extending previous zero-temperature studies.

Findings

At low temperature, gases exhibit properties interpolating between Bose and Fermi gases.

At high temperature, gases behave like spin-polarized fermions.

Tan's contact relates simply to the Tonks-Girardeau gas contact as C=0.5(1-cos(χπ))C_b.

Abstract

We investigate the strongly interacting hard-core anyon gases in a one dimensional harmonic potential at finite temperature by extending thermal Bose-Fermi mapping method to thermal anyon-ferimon mapping method. With thermal anyon-fermion mapping method we obtain the reduced one-body density matrix and therefore the momentum distribution for different statistical parameters and temperatures. At low temperature hard-core anyon gases exhibit the similar properties as those of ground state, which interpolate between Bose-like and Fermi-like continuously with the evolution of statistical properties. At high temperature hard-core anyon gases of different statistical properties display the same reduced one-body density matrix and momentum distribution as those of spin-polarized fermions. The Tan's contact of hard-core anyon gas at finite temperature is also evaluated, which take the simple relation with that of Tonks-Girardeau gas $C_b$ as $C=\frac12(1-cos\chi\pi)C_b$.