  We study the two-dimensional Bose-Hubbard model with anisotropic hopping.
Focusing on the effects of anisotropy on the superfluid properties such like
the helicity modulus and the normal-to-superfluid
(Berezinskii-Kosterlitz-Thouless, BKT) transition temperature, two different
approaches are compared: Large-scale Quantum Monte Carlo simulations and the
self-consistent harmonic approximation (SCHA). For the latter, two different
formulations are considered, one applying near the isotropic limit and the
other applying in the extremely anisotropic limit. Thus we find that the SCHA
provides a reasonable description of superfluid properties of this system
provided the appropriate type of formulation is employed. The accuracy of the
SCHA in the extremely anisotropic limit, where the BKT transition temperature
is tuned to zero (i.e. into a Quantum critical point) and therefore quantum
fluctuations play a dominant role, is particularly striking.
