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

The inhomogeneous extended Bose‐Hubbard model: A mean‐field theory

Jamshid Moradi Kurdestany, R.V. Pai, Rahul Anil Pandit

Abstract We develop an inhomogeneous mean‐field theory for the extended Bose‐Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean‐field theory yields the phase diagram of the homogeneous extended Bose‐Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott‐insulator (MI), density‐wave (DW), and supersolid (SS) phases in the plane of the chemical potential µ and on‐site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest‐neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density‐wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold‐atom dipolar condensates in optical lattices in a confining potential.Abstract We develop an inhomogeneous mean‐field theory for the extended Bose‐Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean‐field theory yields the phase diagram of the homogeneous extended Bose‐Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott‐insulator (MI), density‐wave (DW), and supersolid (SS) phases in the plane of the chemical potential µ and on‐site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest‐neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density‐wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold‐atom dipolar condensates in optical lattices in a confining potential.

arXiv:1201.6451Annalen der PhysikFeb 2, 201220 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.