VERTEX FUNCTION OF A STRONGLY INTERACTING ELECTRON-HOLE PAIR NEAR THE FERMI SURFACE

Abstract

In this work we calculate and compare all the second- and third-order diagrams of the irreducible part K of the electron-hole scattering function for strongly interacting particles near the Fermi surface. We show that the exchange ladder diagrams for K are indeed the most singular diagrams up to this order of perturbation theory in the proximity of the Fermi surface. From this result emerges a new low energy scale parameter and a new effective coupling constant associated with the strongly interacting regime. The summation of exchange ladder diagrams to infinite order produces a purely imaginary pole in K. As a result the vertex function Γ diverges and the Fermi liquid becomes unstable in this strongly interacting regime.