Generic superfluid-insulator transition in the spherical limit in two dimensions

Abstract

The generic superfluid-insulator transition of the quantum rotor model in two dimensions is studied in the spherical limit. The finite-size scaling behaviors of various quantities, such as the correlation length, the superfluid stiffness, the compressibility, and the density, in very large systems, without suffering from statistical errors, are investigated as functions of the tuning parameter and the aspect ratio, which clearly shows that the aspect ratio is also a scaling variable. We find that the transition is characterized by the dynamical critical exponent z = 2.0 and the correlation length critical exponent v = 0.5, which is consistent with the theoretical prediction, indicating the mean-field nature of the transition.