Quantum Critical Behavior of Disordered Hardcore Bosons

We study the finite temperature and zero temperature critical behavior in hard core bosons with (a) uniform (b) disordered and (c) staggered chemical potential. This model can also be thought of as quantum XY model in a transversed magnetic field. Using the directed loop Monte Carlo algorithm on large square lattices, we calculate the pair susceptibility (Xp) and winding susceptibility (Xw). We find the usual Kosterlitz-Thouless (KT) thermal transition in all three cases. At very low temperatures, however, the phase boundary profile in these cases differ from each other. In the zero temperature analysis, we define the exponent for the scaling of Xp near the critical Mu to be 2beta, and similarly, the exponent for Xw to be Nu. In the uniform case, the exponents are expected to be mean field beta=0.5, Nu=1). Even at Mu of order 98% of the critical Mu and for lattices as large as 96x96, we see deviation from mean field behavior. For the lattices we have explored the curvature in our data suggests that the (beta<0.5, Nu<1) in the uniform case and (beta>=0.5, Nu>=1) in the disordered case.