Ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping

TL;DR

This study maps the ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping, revealing how the phase boundary and universality class relate to the 1d limit and isotropic 2d system, with implications for cold gas experiments.

Contribution

It provides the first comprehensive quantum Monte Carlo analysis connecting 1d and 2d Bose-Hubbard models with anisotropic hopping, including analytical derivations of phase boundary behavior.

Findings

The tip of the Mott lobe follows a curve controlled by the 1d limit across all anisotropies.

The universality class remains consistent with the isotropic 2d system.

Phase boundaries for strong anisotropy align with 1d system predictions.

Abstract

We compute the ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping using quantum Monte Carlo simulations, connecting the 1d to the 2d system. We find that the tip of the lobe lies on a curve controlled by the 1d limit over the full anisotropy range while the universality class is always the same as in the isotropic 2d system. This behavior can be derived analytically from the lowest RG equations and has a form typical for the underlying Kosterlitz-Thouless transition in 1d. We also compute the phase boundary of the Mott lobe for strong anisotropy and compare it to the 1d system. Our calculations shed light on recent cold gas experiments monitoring the dynamics of an expanding cloud.