The flow equation approach to the pairing instability problem

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.