A Framework for Studying a Quantum Critical Metal in the Limit $N_f\rightarrow0$

TL;DR

This paper develops a non-perturbative framework to analyze a 2D quantum critical metal with a spherical Fermi surface in the limit of vanishing fermion flavors, revealing exponential decay in Friedel oscillations.

Contribution

It introduces a novel non-perturbative method for calculating fermion correlation functions in a quantum critical metal at the limit $N_f ightarrow0$ and large Fermi surface.

Findings

Exponential decay of Friedel oscillations in the correlation function.

Framework applicable to non-perturbative studies of quantum critical metals.

Abstract

We study a model in 1+2 dimensions composed of a spherical Fermi surface of $N_f$ flavors of fermions coupled to a massless scalar. We present a framework to non-perturbatively calculate general fermion $n$-point functions of this theory in the limit $N_f\rightarrow0$ followed by $k_F\rightarrow\infty$ where $k_F$ sets both the size and curvature of the Fermi surface. Using this framework we calculate the zero-temperature fermion density-density correlation function in real space and find an exponential decay of Friedel oscillations.