Simulating the Berezinskii-Kosterlitz-Thouless Transition with Complex Langevin

Abstract

Numerical simulations of the full quantum properties of interacting many-body systems by means of field-theoretic Monte-Carlo techniques are often limited due to a sign problem. Here we simulate properties of a dilute two-dimensional Bose gas in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) transition by means of the Complex Langevin (CL) algorithm, thereby extending our previous CL study of the three-dimensional Bose gas to the lower-dimensional case. The purpose of the paper is twofold. On the one hand, it adds to benchmarking of the CL method and thus contributes to further exploring the range of applicability of the method. With the respective results, the universality of the equation of state is recovered, as well as the long-wave-length power-law dependence of the single-particle momentum spectrum below the BKT transition. Analysis of the rotational part of the current density corroborates vortex unbinding in crossing the transition. Beyond these measures of consistency we compute quantum corrections to the critical density and chemical potential in the weakly coupled regime. Our results show a shift of these quantities to lower values as compared to those obtained from classical field theory. It points in the opposite direction as compared to the shift of the critical density found by means of the path-integral Monte-Carlo method at larger values of the coupling. Our simulations widen the perspective for precision comparisons with experiment.