Berezinskii-Kosterlitz-Thouless transition of two-dimensional Bose gases in a synthetic magnetic field

We study the field dependency of the Berezinskii-Kosterlitz-Thouless transition temperature T_c(H) of Bose gases in a two-dimensional optical lattice in the synthetic magnetic field using the Metropolis Monte Carlo method. The system is described by the frustrated XY model and the critical temperature is determined through observing the disappearance of the central peak of the momentum distribution of the gas, which can be directly measured by the time-of-flight absorbing imaging in cold-atom experiments. T_c(H) is found to exhibit a largest peak at the fraction of a flux quantum f=φ/φ₀=1/2 and a second-largest one at f=1/3, in agreement with former studies on superconducting Josephson arrays. We also indicate that the synthetic magnetic field experiment can produce strong enough frustration for exploring the physics of the frustrated XY model.