Strong-coupling perturbation theory for the extended Bose-Hubbard model

TL;DR

This paper introduces a strong-coupling perturbation theory for the extended Bose-Hubbard model, providing analytical phase boundary expressions for various insulating and conducting phases, with implications for ultracold dipolar gases in optical lattices.

Contribution

It develops a third-order perturbation theory for the extended Bose-Hubbard model, deriving analytical phase boundaries for complex quantum phases.

Findings

Analytical expressions for phase boundaries are obtained up to third order in hopping.

Results apply to hypercubic lattices in more than one dimension.

Implications discussed for ultracold dipolar Bose gases in optical lattices.

Abstract

We develop a strong-coupling perturbation theory for the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on ($d > 1$)-dimensional hypercubic lattices. Analytical expressions for the ground-state phase boundaries between the incompressible (Mott or charge-density-wave insulators) and the compressible (superfluid or supersolid) phases are derived up to third order in the hopping $t$. We also briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.