Quantum critical metals in $d=3+1$

TL;DR

This paper investigates the behavior of disorder-free metals near a 3+1 dimensional Ising nematic quantum critical point, revealing a regime where fermions exhibit marginal Fermi liquid behavior with enhanced decay rates.

Contribution

It introduces a large N theoretical framework that enhances marginal Fermi liquid behavior while suppressing Landau damping effects in 3+1 dimensions.

Findings

Fermions show linear-in-frequency imaginary self-energy above damping scale

Perturbation theory breaks down below Landau damping scale

Large N theory enhances marginal Fermi liquid features

Abstract

We study the problem of disorder-free metals near a continuous Ising nematic quantum critical point in $d=3+1$ dimensions. We begin with perturbation theory in the `Yukawa' coupling between the electrons and undamped bosons (nematic order parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the `marginal Fermi liquid' phenomenology\cite{Varma}. We discuss a large N theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.