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Superfluid to normal phase transition in strongly interacting bosons in two and three dimensions.

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Using quantum Monte Carlo simulations, we investigate the
finite-temperature phase diagram of hard-core bosons (XY model) in

two- and three-dimensional square lattices. To determine
the phase boundaries, we perform a finite-size scaling analysis of the
condensate fraction and/or the superfluid stiffness. We then discuss how this
diagrams can be measured in experiments with trapped ultracold gases, where the
systems are inhomogeneous. For that, we introduce a method based on the
measurement of the zero-momentum occupation, which is adequate for experiments dealing
with both homogeneous and trapped systems. Finally, we provide an analytical
argument that demonstrates that the Bose-Hubbard model does not exhibit
finite-temperature BEC in two dimensions, provided that density remains finite
across the entire system in the thermodynamic limit.