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Phase diagram of the quantum O(2)-model in 2+1 dimensions

The quantum O(2) model in 2+1 dimensions is studied by simulating the 3d O(2) model near criticality. Finite densities are introduced by a non-zero chemical potential mu, and the worm algorithm is used to circumvent the sign problem. The renormalisation is discussed in some detail. We find that the onset value of the chemical potential coincides with the mass gap. The mu-dependence of the density rules out Bose-Einstein condensation and might be compatible with an interacting Fermi gas. The mu-T phase diagram is explored using the density and the magnetic susceptibility. In the cold, but dense regime of the phase diagram, we find a superfluid phase.