Flow equation approach to the pairing problems

TL;DR

This paper employs the flow equation method to analyze fermion pairing, revealing how interactions lead to either BCS-like gaps or symmetry-preserving spectra, with extensions to fermion-boson interactions and quantum fluctuations.

Contribution

It introduces a continuous Bogoliubov transformation scheme resembling renormalization group methods for pairing problems, including fermion-boson interactions and quantum fluctuation effects.

Findings

Flow equations produce BCS and gapped spectra.

Quantum fluctuations induce a gap centered on boson energy.

Bose-Einstein condensation transitions the spectrum to BCS form.

Abstract

We apply the flow equation method for studying the fermion systems where pairing interactions can either trigger the BCS instability with the symmetry breaking manifested by the off-diagonal order parameter or lead to the gaped single particle spectrum without any symmetry breaking. We construct the continuous Bogoliubov transformation in a scheme resembling the renormalization group procedure. We further extend this continuous transformation to a case where fermion pairs interact with the boson field. Due to temporal quantum fluctuations the single particle excitation spectrum develops a gap which is centered around the renormalized boson energy. When bosons undergo the Bose Einstein condensation this structure evolves into the BCS spectrum.