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arXiv:1002.4735

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

Saeed Ghanbari, Joel Frederick Corney, Tien D. Kieu

Published Feb 25, 2010• 1 citation
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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.

DOI
10.48550/arxiv.1002.4735

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Finite temperature correlations in the Bose-Hubbard model: application of the Gauge PPP representation
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 PPP representation. We study various quantities including the Luttinger parameter KKK, 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≈0.1UT \approx 0.1 UT≈0.1U. Also, at chemical potential μ=0.5Uμ=0.5 Uμ=0.5U and temperature T=0.5UT=0.5 UT=0.5U by increasing JJJ, the relative value of the number fluctuation decreases and approaches that of a coherent state.
We simulate quantum degenerate Bose gases at finite temperatures in a grand canonical ensemble and use the Bose-Hubbard model which can describe the dynamics of ultracold bosonic atoms in optical and magnetic lattices. We study ultracold atoms with the gauge P-representation in 1D with 1, 2 (double well), 3, 7 and 11 sites and study quantum correlations and other physical quantities at different temperatures across the superfluid to Mott insulator quantum phase transition. Moreover, using a truncated number-state basis and the gauge P-representation, we show that the Mott lobes are not present unless the temperature is below a certain value.
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