Finite temperature correlations in the Bose-Hubbard model: application of the Gauge $P$ representation

Saeed Ghanbari; Joel F. Corney; Tien D. Kieu

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arXiv · 1002.4735

Finite temperature correlations in the Bose-Hubbard model: application of the Gauge $P$ representation

Saeed Ghanbari·Joel F. Corney·Tien D. Kieu

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Abstract

We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1D and at finite temperature, we simulate ultracold Bose gases in imaginary time with the gauge $P$ representation. We study various quantities including the Luttinger parameter $K$, which is important for locating the boundaries of the Mott insulator lobes, and find a simple relation for the kinetic energy part of the Bose-Hubbard Hamiltonian. We show that for J=0, the stepwise pattern of the average number of particles per lattice site versus the chemical potential vanishes at temperatures above $T \approx 0.1 U$. Also, at chemical potential $μ=0.5 U$ and temperature $T=0.5 U$ by increasing $J$, the relative value of the number fluctuation decreases and approaches that of a coherent state.

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BibTeX RIS

Saeed Ghanbari, Joel F. Corney, Tien D. Kieu. 2010-02-25. Finite temperature correlations in the Bose-Hubbard model: application of the Gauge $P$ representation. https://arxiv.org/abs/1002.4735

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