On self-energy contributions near Berezinskii-Kosterlitz-Thouless transition in interacting homogeneous 2D Bose system

We explore the consequences of including quantum corrections in an interacting 2D Bose system near Berezinskii-Kosterlitz-Thouless (BKT) transition. To go beyond mean-field theory and treat correlations, we use Matsubara Green's function method, and, following a previous novel approach, study features of the interacting Green's function just above the transition. We numerically obtain self-consistent solutions of boson self-energy to second order as well as higher order (re-summation of ladder and bubble diagrams) in the interaction strength, for the entire range of momentum, k, and compare our findings with analytic results in the limits of low- and high-k. Thereby, in the weak interaction limit, we retrieve the universal transition condition and calculate the universal scaling parameter (independent of interaction strength). The renormalised single-particle Green's function is found to decay algebraically at large distance r.