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

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.