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

Abstract

We study a model in 1+2 dimensions composed of a spherical Fermi surface of N_fNf flavors of fermions coupled to a massless scalar. We present a framework to non-perturbatively calculate general fermion nn-point functions of this theory in the limit N_f\rightarrow0Nf→0 followed by k_F\rightarrow\inftykF→∞ where k_FkF 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.