Exact electronic Green functions in a Luttinger liquid with long-range interactions

Abstract

We compute the two-point (equal-time) electronic Green function in a Tomonaga-Luttinger system with long-range electron-electron interactions. We obtain an analytical expression for a “super long-range” potential of the form V(x) = e²d^-∈/|x|^1-∈. As a consistency check of our computational technique we also consider the particular case of a Coulomb potential. Our result confirms the -C(log x)^3/2 long-distance behavior first obtained by Schulz.