Standard basis operator method for ground-state and temperature properties of the single- and two-component Bose-Hubbard models

We formulate an improved standard basis operator (SBO) method for the single and two-component Bose-Hubbard model in three dimensions. In the first case, nonzero temperature predictions are qualitatively and quantitatively enhanced by taking into account necessary number of on-site states, not just three as in previous works. Performance of the final numerical calculations is also improved by asymptotic analysis of the self-consistent equations near the critical line. Obtained results are compared with Monte-Carlo, tensor networks, Quantum Rotor Approach and experimental data. In the two-component case, SBO generalizes rather poorly, being able to account for intra-species thermal and quantum fluctuations, but not the inter-species ones. Deeper reasons for this situation are discussed. Still however, non-trivial deformation of the phase diagrams is predicted, together with first-order phase transitions steered by the changes in chemical potential.