Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory

TL;DR

This paper uses a non-perturbative renormalization-group method to unify Bogoliubov's approximation and Popov's hydrodynamic theory, revealing the behavior of superfluid excitations in two-dimensional bosons at zero temperature.

Contribution

It provides a comprehensive, non-perturbative analysis connecting two fundamental theories of superfluidity in 2D bosonic systems.

Findings

Anomalous self-energy exhibits a square root singularity below momentum scale k_G.

Goldstone mode coexists with a continuum of excitations below k_G.

Results unify Bogoliubov and Popov theories for superfluidity.

Abstract

Using a non-perturbative renormalization-group technique, we compute the momentum and frequency dependence of the anomalous self-energy and the one-particle spectral function of two-dimensional interacting bosons at zero temperature. Below a characteristic momentum scale $k_G$, where the Bogoliubov approximation breaks down, the anomalous self-energy develops a square root singularity and the Goldstone mode of the superfluid phase (Bogoliubov sound mode) coexists with a continuum of excitations, in agreement with the predictions of Popov's hydrodynamic theory. Thus our results provide a unified picture of superfluidity in interacting boson systems and connect Bogoliubov's theory (valid for momenta larger than $k_G$) to Popov's hydrodynamic approach.