Instabilities of quantum critical metals in the limit $N_f\rightarrow0$

TL;DR

This paper investigates the behavior of quantum critical metals with a small number of fermion flavors, revealing how fluctuations influence quasiparticles, pairing, and density wave instabilities in a 2+1D model.

Contribution

It provides a non-perturbative analysis of fermion correlations and susceptibilities near quantum critical points in the limit of zero fermion flavors, including effects of diagram restoration.

Findings

Fluctuations smear quasiparticles but can enhance pairing.

Quantum critical points can induce spin and charge density wave instabilities.

Restoring certain diagrams does not alter long-range correlator behavior except at QCPs.

Abstract

We study a model in 2+1 dimensions composed of a Fermi surface of $N_f$ flavors of fermions coupled to scalar fluctuations near quantum critical points (QCPs). The $N_f\rightarrow0$ limit allows us to non-perturbatively calculate the long-range behavior of fermion correlation functions. We use this to calculate charge, spin and pair susceptibilities near different QCPs at zero and finite temperatures, with zero and finite order parameter gaps. While fluctuations smear out the fermionic quasiparticles, we find QCPs where the overall effect of fluctuations leads to enhanced pairing. We also find QCPs where the fluctuations induce spin and charge density wave instabilities for a finite interval of order parameter fluctuation gaps at $T=0$. We restore a subset of the diagrams suppressed in the $N_f\rightarrow0$ limit, all diagrams with internal fermion loops with at most 2 vertices, and find that this does not change the long-range behavior of correlators except right at the QCPs.