Spectral Function and Quasiparticle Damping of Interacting Bosons in Two Dimensions

Abstract

We employ the functional renormalization group to study dynamical properties of the two-dimensional Bose gas. Our approach is free of infrared divergences, which plague the usual diagrammatic approaches, and is consistent with the exact Nepomnyashchy identity, which states that the anomalous self-energy vanishes at zero frequency and momentum. We recover the correct infrared behavior of the propagators and present explicit results for the spectral line shape, from which we extract the quasiparticle dispersion and damping.

Infrared behavior of interacting bosons at zero temperature

“…12,13,16,17,18,14,15,19,20 The strategy of the NPRG is to build a family of theories indexed by a momentum scale k such that fluctuations are smoothly taken into account as k is lowered from the microscopic scale Λ down to 0. 25,26 This is achieved by adding to the action (1) an infrared regulator term…”

“…3, we discuss the non-perturbative renormalization group (NPRG) and show how it enables to obtain the exact infrared behavior of the normal and anomalous single-particle propagators without encountering infrared divergences. 12,13,14,15,16,17,18,19,20 …”

Real-time correlation functions in the $$O(N)$$ O ( N ) model from the functional renormalization group

“…Spectral functions have been calculated with the FRG in non-relativistic models using different truncation schemes including the "BMW" approximation [24,25], vertex expansions or derivative expansions [26][27][28]. In all these cases, however, the spectral functions were reconstructed from Euclidean 2-point correlators via analytic continuation using Padé approximants.…”

Analytic continuation of functional renormalization group equations

“…Methods based for example on Padé approximants need information from many Matsubara frequencies and the numerical effort gets rather large. Nevertheless, this approach has been successfully followed in the past and allowed to calculate for example the spectral function of non-relativistic bosons in two spatial dimensions [39,40].…”

“…In refs. [39] and [40], the truncated renormalization group equations for a two-dimensional gas of non-relativistic bosons have been solved in the Matsubara formalism with imaginary frequencies. The result for the propagator at the macroscopic scale k = 0 has then been analytically continued to real frequencies using numerical Padé JHEP05(2012)021 approximant techniques.…”