Infrared behavior of interacting bosons at zero temperature

TL;DR

This paper reviews the infrared properties of zero-temperature interacting bosons, discussing theoretical approaches that overcome divergences and linking superfluid behavior to phase transitions in the Bose-Hubbard model.

Contribution

It compares two divergence-free methods, Popov's hydrodynamic theory and the non-perturbative renormalization group, to determine exact infrared behavior of correlation functions.

Findings

Identifies limitations of Bogoliubov approximation due to infrared divergences.

Introduces divergence-free approaches for accurate correlation function analysis.

Connects superfluid infrared behavior to the superfluid--Mott-insulator transition.

Abstract

We review the infrared behavior of interacting bosons at zero temperature. After a brief discussion of the Bogoliubov approximation and the breakdown of perturbation theory due to infrared divergences, we present two approaches that are free of infrared divergences -- Popov's hydrodynamic theory and the non-perturbative renormalization group -- and allow us to obtain the exact infrared behavior of the correlation functions. We also point out the connection between the infrared behavior in the superfluid phase and the critical behavior at the superfluid--Mott-insulator transition in the Bose-Hubbard model.