Abstract

We study finite-temperature properties of the strongly interacting bosons in three-dimensional lattices by employing the combined Bogoliubov method and the quantum rotor approach. Based on the mapping of the Bose–Hubbard Hamiltonian of strongly interacting bosons onto U(1) phase action, we study their thermodynamic phase diagrams for several lattice geometries including simple cubic, body, as well as face-centered lattices. The quantitative values for the phase boundaries obtained here may be used as a reference for emulation of the Bose–Hubbard model on a variety of optical lattice structures in order to demonstrate experimental-theoretical consistency for the numerical values regarding the location of the critical points.

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