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We study finite-temperature phase structures of hard-core bosons in atwo-dimensional optical lattice subject to an effective magnetic field byemploying the gauged CP$^1$ model. Based on the extensive Monte Carlosimulations, we study their phase structures at finite temperatures for severalvalues of the magnetic flux per plaquette of the lattice and mean particledensity. Despite the presence of the particle number fluctuation, thethermodynamic properties are qualitatively similar to those of the frustratedXY model with only the phase as a dynamical variable. This suggests that coldatom simulators of the frustrated XY model are available irrespective of theparticle filling at each site.

Finite-temperature phase structures of hard-core bosons in an optical lattice with an effective magnetic field