Non-perturbative emergence of non-Fermi liquid behaviour in $d=2$ quantum critical metals

TL;DR

This paper provides an exact non-perturbative analysis of a $d=2$ fermionic system coupled to a critical boson, revealing non-Fermi liquid behavior with unique spectral features at different Fermi surfaces.

Contribution

It introduces a non-perturbative solution for the fermion spectral function in a $d=2$ quantum critical metal using the quenched approximation, uncovering non-Fermi liquid spectra.

Findings

Spectral functions exhibit non-Fermi liquid power-law scaling.

Identifies three distinct low-energy excitations at different Fermi surfaces.

Reveals continuous spectral weight without quasiparticle poles.

Abstract

We consider the planar local patch approximation of $d=2$ fermions at finite density coupled to a critical boson. In the quenched or Bloch-Nordsieck approximation, where one takes the limit of fermion flavors $N_f\rightarrow 0$, the fermion spectral function can be determined {exactly}. We show that one can obtain this non-perturbative answer thanks to a specific identity of fermionic two-point functions in the planar local patch approximation. The resulting spectrum is that of a non-Fermi liquid: quasiparticles are not part of the exact fermionic excitation spectrum of the theory. Instead one finds continuous spectral weight with power law scaling excitations as in a $d=1$ dimensional critical state. Moreover, at low energies there are three such excitations at three different Fermi surfaces, two with a low energy Green's function $G \sim (\omega-v_*k)^{-1/2}$ and one with $G \sim |\omega+k|^{-1/3}$.