Infrared Behavior of Interacting Bosons at Zero Temperature

TL;DR

This paper uses symmetry principles to solve longstanding issues in the theory of interacting bosons at zero temperature, revealing exact behaviors of quasiparticles and correlation functions across different dimensions.

Contribution

It introduces a symmetry-based approach that constrains renormalizations, providing exact results for quasiparticles and correlation functions in various dimensions.

Findings

For d>3, Bogoliubov quasiparticles are exact.

For 1<d<=3, the theory predicts a nontrivial solution with exact singular correlation exponents.

Phonons remain the low-energy excitations across dimensions.

Abstract

We exploit the symmetries associated with the stability of the superfluid phase to solve the long-standing problem of interacting bosons in the presence of a condensate at zero temperature. Implementation of these symmetries poses strong conditions on the renormalizations that heal the singularities of perturbation theory. The renormalized theory gives: For d>3 the Bogoliubov quasiparticles as an exact result; for 1<d<=3 a nontrivial solution with the exact exponent for the singular longitudinal correlation function, with phonons again as low-lying excitations.