Interacting fermions in two dimensions: beyond the perturbation theory

TL;DR

This paper investigates the failure of perturbation theory for 2D fermions with short-range interactions, revealing divergence issues due to zero-sound modes and providing a resummed self-energy analysis.

Contribution

It demonstrates the divergence of perturbation theory near the mass shell and develops a resummation method to accurately describe the self-energy in 2D fermion systems.

Findings

Perturbation series diverges near the mass shell for 2D fermions.

Resummation yields a finite self-energy and spectral function features.

Zero sound interactions do not alter the T^2 specific heat term.

Abstract

We consider a system of 2D fermions with short-range interaction. A straightforward perturbation theory is shown to be ill-defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. We show that the divergences result from the interaction of fermions with the zero-sound collective mode. By re-summing the most divergent diagrams, we obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. We also show that the interaction with the zero sound does not affect a non-analytic, $T^{2}$-part of the specific heat.