The Inhomogeneous Extended Bose-Hubbard Model: A Mean-Field Theory

TL;DR

This paper develops a mean-field theory for the inhomogeneous extended Bose-Hubbard model with a confining potential, revealing complex phase structures like shells of superfluid, Mott-insulator, density-wave, and supersolid phases relevant for cold-atom experiments.

Contribution

It introduces an inhomogeneous mean-field approach that captures spatially varying phases in the extended Bose-Hubbard model with a trap, extending previous homogeneous models.

Findings

Phase diagrams for homogeneous model with various V values.

Nonuniform superfluid and density-wave order parameters in traps.

Spherical shells of different phases in the presence of 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 (\mu) 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