Fermionic propagators for 2D systems with singular interactions

TL;DR

This paper investigates the fermionic propagator in 2D systems with singular interactions, revealing how the pole structure varies with the number of fermionic species and analyzing the crossover between different regimes.

Contribution

It provides a detailed analysis of the fermionic propagator behavior across different coupling regimes, especially the survival of the pole at small N and the crossover from pole to regular behavior.

Findings

The pole in the propagator persists for all N.

At small N, the pole exists only near the mass shell within O(N^2).

At large N, the propagator exhibits a pole, while at N=0 it is regular everywhere.

Abstract

We analyze the form of the fermionic propagator for 2D fermions interacting with massless overdamped bosons. Examples include a nematic and Ising ferromagnetic quantum-critical points, and fermions at a half-filled Landau level. Fermi liquid behavior in these systems is broken at criticality by a singular self-energy, but the Fermi surface remains well defined. These are strong-coupling problems with no expansion parameter other than the number of fermionic species, N. The two known limits, N >>1 and N=0 show qualitatively different behavior of the fermionic propagator G(\epsilon_k, \omega). In the first limit, G(\epsilon_k, \omega) has a pole at some \epsilon_k, in the other it is analytic. We analyze the crossover between the two limits. We show that the pole survives for all N, but at small N it only exists in a range O(N^2) near the mass shell. At larger distances from the mass shell, the system evolves and G(\epsilon_k, \omega) becomes regular. At N=0, the range where the pole exists collapses and G(\epsilon_k, \omega) becomes regular everywhere.