We derive the $\mathrm{Bogoliubov}+U$ formalism to study the thermodynamical properties of the Bose-Hubbard model. The framework can be viewed as the zero-frequency limit of bosonic dynamical mean-field theory (B-DMFT), but equally well as an extension of the mean-field decoupling approximation in which pair creation and annihilation of depleted particles is taken into account. The self-energy on the impurity site is treated variationally, minimizing the grand potential. The theory containing just three parameters that are determined self-consistently reproduces the $T=0$ phase diagrams of the three-dimensional and two-dimensional Bose-Hubbard model with an accuracy of $1%$ or better. The superfluid to normal transition at finite temperature is also reproduced well and only slightly less accurately than in B-DMFT.We derive the $\mathrm{Bogoliubov}+U$ formalism to study the thermodynamical properties of the Bose-Hubbard model. The framework can be viewed as the zero-frequency limit of bosonic dynamical mean-field theory (B-DMFT), but equally well as an extension of the mean-field decoupling approximation in which pair creation and annihilation of depleted particles is taken into account. The self-energy on the impurity site is treated variationally, minimizing the grand potential. The theory containing just three parameters that are determined self-consistently reproduces the $T=0$ phase diagrams of the three-dimensional and two-dimensional Bose-Hubbard model with an accuracy of $1%$ or better. The superfluid to normal transition at finite temperature is also reproduced well and only slightly less accurately than in B-DMFT.

arXiv:1501.07849Physical Review BJun 22, 20156 citations

We derive the

\mathrm{Bogoliubov}+U

formalism to study the thermodynamical properties of the Bose-Hubbard model. The framework can be viewed as the zero-frequency limit of bosonic dynamical mean-field theory (B-DMFT), but equally well as an extension of the mean-field decoupling approximation in which pair creation and annihilation of depleted particles is taken into account. The self-energy on the impurity site is treated variationally, minimizing the grand potential. The theory containing just three parameters that are determined self-consistently reproduces the

T=0

phase diagrams of the three-dimensional and two-dimensional Bose-Hubbard model with an accuracy of

1%

or better. The superfluid to normal transition at finite temperature is also reproduced well and only slightly less accurately than in B-DMFT.