Article,
Infrared behavior and spectral function of a Bose superfluid at zero temperature
Physical Review A, (October 2009)
DOI: 10.1103/physreva.80.043627
Abstract
In a Bose superfluid, the coupling between transverse (phase) and longitudinal fluctuations leads to a divergence of the longitudinal correlation function, which is responsible for the occurrence of infrared divergences in the perturbation theory and the breakdown of the Bogoliubov approximation. We report a nonperturbative renormalization-group calculation of the one-particle Green's function of an interacting boson system at zero temperature. We find two regimes separated by a characteristic momentum scale kG ( ” Ginzburg” scale). While the Bogoliubov approximation is valid at large momenta and energies, |p|, |ω|/c⪢kG (with c as the velocity of the Bogoliubov sound mode), in the infrared (hydrodynamic) regime, |p|, |ω|/c⪡kG, the normal and anomalous self-energies exhibit singularities reflecting the divergence of the longitudinal correlation function. In particular, we find that the anomalous self-energy agrees with the Bogoliubov result Σan(p,ω)≃const at high energies and behaves as Σan(p,ω)∼(c2p2−ω2)(d−3)/2 in the infrared regime (with d as the space dimension), in agreement with the Nepomnyashchii identity Σan(0,0)=0 and the predictions of Popov's hydrodynamic theory. We argue that the hydrodynamic limit of the one-particle Green's function is fully determined by the knowledge of the exponent 3−d characterizing the divergence of the longitudinal susceptibility and the Ward identities associated to gauge and Galilean invariances. The infrared singularity of Σan(p,ω) leads to a continuum of excitations (coexisting with the sound mode) which shows up in the one-particle spectral function.
