Momentum distribution of the insulating phases of the extended Bose-Hubbard model

TL;DR

This paper introduces two methods to calculate the momentum distribution of insulating phases in the extended Bose-Hubbard model, providing insights relevant for ultracold dipolar Bose gases in optical lattices.

Contribution

It develops both a random phase approximation and a strong-coupling perturbation approach to analyze momentum distributions in various dimensions.

Findings

RPA matches exact infinite-dimensional solution

Strong-coupling expansion effective in 2D and 3D

Results applicable to ultracold dipolar Bose gases

Abstract

We develop two methods to calculate the momentum distribution of the insulating (Mott and charge-density-wave) phases of the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on $d$-dimensional hypercubic lattices. First we construct the random phase approximation result, which corresponds to the exact solution for the infinite-dimensional limit. Then we perform a power-series expansion in the hopping $t$ via strong-coupling perturbation theory, to evaluate the momentum distribution in two and three dimensions; we also use the strong-coupling theory to verify the random phase approximation solution in infinite dimensions. Finally, we briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.