  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.
