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

摘要

Using a non-perturbative renormalization-group technique, we compute themomentum and frequency dependence of the anomalous self-energy and theone-particle spectral function of two-dimensional interacting bosons at zerotemperature. Below a characteristic momentum scale $k_G$, where the Bogoliubovapproximation breaks down, the anomalous self-energy develops a square rootsingularity and the Goldstone mode of the superfluid phase (Bogoliubov soundmode) coexists with a continuum of excitations, in agreement with thepredictions of Popov's hydrodynamic theory. Thus our results provide a unifiedpicture of superfluidity in interacting boson systems and connect Bogoliubov'stheory (valid for momenta larger than $k_G$) to Popov's hydrodynamic approach.