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

Abstract

ABSTRACT 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.