Phase Stability in the Two dimensional Anisotropic Boson Hubbard Hamiltonian

TL;DR

This paper investigates whether anisotropic hopping or interactions in a 2D boson Hubbard model can stabilize a supersolid phase, but finds that phase separation persists across different anisotropy configurations.

Contribution

The study explores the effects of anisotropic hopping and interactions on phase stability in the 2D boson Hubbard model, concluding that phase separation remains dominant.

Findings

Anisotropy does not stabilize supersolid phase in the model.

Phase separation persists despite anisotropic modifications.

Charge density wave and superfluid coexistence are not stabilized by anisotropy.

Abstract

The two dimensional square lattice hard-core boson Hubbard model with near neighbor interactions has a `checkerboard' charge density wave insulating phase at half-filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $\hat x$ and $\hat y$ directions, we conclude that phase separation still occurs.