Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model

B. Capogrosso-Sansone; N. V. Prokof'ev; B. V. Svistunov

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Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model

B. Capogrosso-Sansone·N. V. Prokof'ev·B. V. Svistunov

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Abstract

We report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantly higher accuracy than it has been done in the past. In particular, the position of the critical point at filling factor n=1 is found to be at (U/t)_c = 29.34(2), and the insulating gap Delta is measured with accuracy of a few percent of the hopping amplitude t. We obtain the effective mass of particle and hole excitations in the insulating state--with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip--along with the sound velocity in the strongly correlated superfluid phase. These parameters are the necessary ingredients to perform analytic estimates of the low temperature (T << Delta) thermodynamics in macroscopic samples. We present accurate thermodynamic curves, including these for specific heat and entropy, for typical insulating (U/t=40) and superfluid (t/U=0.0385) phases. Our data can serve as a basis for accurate experimental thermometry, and a guide for appropriate initial conditions if one attempts to use interacting bosons in quantum information processing.

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B. Capogrosso-Sansone, N. V. Prokof'ev, B. V. Svistunov. 2007-01-09. Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model. https://arxiv.org/abs/cond-mat/0701178

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