Application of the renormalization group technique to the problem of phase transition in one-dimensional metallic systems. I. Invariant couplings, vertex, and one-particle Green's function

Abstract

A one-dimensional system of electrons interacting via a BCS-type interaction is investigated by renormalization group techniques in two successive approximations atT=0, keeping only a single energy variable ω. The first approximation is equivalent to the summation of leading logarithmic terms carried out by Bychkovet al., and correspondingly the vertex function displays a singularity at a finite value of ω. The second approximation accounts for the next leading logarithmic terms as well, and by this means the singularity is shown to be pushed down to ω=0. Due to important self-energy contributions, however, the invariant couplings behave differently and tend to a saturation value at ω=0.