Ground-state parameters, finite-size scaling, and low-temperature properties of the two-dimensional $S=\frac{1}{2}$ $\mathrm{XY}$ model

We present high-precision quantum Monte Carlo results for the $S=\frac{1}{2}$ $\mathrm{XY}$ model on a two-dimensional square lattice, in the ground state as well as at finite temperature. The energy, the spin stiffness, the magnetization, and the susceptibility are calculated and extrapolated to the thermodynamic limit. For the ground state, we test a variety of finite-size scaling predictions of effective Lagrangian theory and find good agreement and consistency between the finite-size corrections for different quantities. The low-temperature behavior of the susceptibility and the internal energy is also in good agreement with theoretical predictions.