Ground state properties of a Tonks-Girardeau Gas in a periodic potential

TL;DR

This study numerically investigates the ground-state properties of a Tonks-Girardeau gas in a one-dimensional periodic potential, revealing the absence of Bose-Einstein Condensation and identifying universal scaling relations.

Contribution

It provides the first detailed numerical analysis of the occupation number scaling and orbital properties of a TG gas in periodic potentials, highlighting universal relations.

Findings

No Bose-Einstein Condensation in the system.

Distinct scaling exponents for commensurate and incommensurate cases.

Universal relation among the scaling exponents.

Abstract

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.