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

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

2008-12-06

arxiv.org/abs/0812.1277v1

Physics

Condensed Matter

Statistical Mechanics

7 pages

Scientific paper

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=41 bosons. Then we are able to study the scaling behavior of the occupation numbers of the most dominant orbital for both commensurate and non-commensurate cases, which correspond to an insulating phase and a conducting phase, respectively. We find that, in the commensurate case, the fractional occupation decays as $f_0 \propto 1/\ln N$ with the particle number, while $f_0 \propto 1/N^{0.44}$ in the non-commensurate case. So there is no BEC in both cases. The study of zero momentum peaks shows that $n(0)\propto N$ in commensurate case, which implies that all bonons are localized in the insulating phase.

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