The flow equation approach to the pairing instability problem

TL;DR

This paper introduces a flow equation approach using continuous unitary transformations to analyze pairing instabilities and symmetry breaking in interacting fermion systems, revealing complex phases with incoherent pairs and suppressed density of states.

Contribution

It develops a generalized Bogoliubov transformation within a flow equation framework to distinguish between pairing and superconductivity, highlighting the role of quantum fluctuations.

Findings

Quantum fluctuations can destroy long-range order without breaking pairs.

Existence of incoherent or damped fermion pairs at certain temperatures.

Partial suppression of the density of states near the Fermi energy.

Abstract

By means of the continuous unitary transformation similar to a general scheme of the Renormalization Group (RG) procedure we study the issue of symmetry breaking and pairing instability in the system of interacting fermions. Constructing a generalized version of the Bogoliubov transformation we show that formation of the fermion pairs and their superconductivity/superfluidity can appear at different temperatures. It is shown that strong quantum fluctuations can destroy the long-range order without breaking the fermion pairs which may still exist as incoherent and/or damped entities. Such unusual phase is characterized by a partial suppression of the density of states near the Fermi energy and by residual collective features like the sound-wave mode in the fermion pair spectrum.