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

We study finite-temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to an effective magnetic field by employing the gauged CP¹ model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated $XY$ model, with only the phase as a dynamical variable. This suggests that cold-atom simulators of the frustrated $XY$ model are available irrespective of the particle filling at each site.