# Two dimensional non-Fermi liquid metals: a solvable large N limit

## TL;DR

This paper introduces a solvable large N limit for two-dimensional non-Fermi liquid metals by employing a matrix large N approach, revealing a coupled system of overdamped bosons and non-Fermi liquids with specific dynamical properties.

## Contribution

The authors propose a new large N framework with fermions in the fundamental and order parameters in the adjoint representation, enabling tractable analysis of 2D NFL metals.

## Key findings

- System exhibits overdamped bosons with z=3
- Non-Fermi liquid self-energy scales as ω^{2/3}
- Approach overcomes previous breakdown issues in 2D

## Abstract

Significant effort has been devoted to the study of "non-Fermi liquid" (NFL) metals: gapless conducting systems that lack a quasiparticle description. One class of NFL metals involves a finite density of fermions interacting with soft order parameter fluctuations near a quantum critical point. The problem has been extensively studied in a large N limit (N corresponding to the number of fermion flavors) where universal behavior can be obtained by solving a set of coupled saddle-point equations. However a remarkable study by S.-S.~Lee revealed the breakdown of such approximations in two spatial dimensions. We show that an alternate approach, in which the fermions belong to the fundamental representation of a global SU(N) flavor symmetry, while the order parameter fields transform under the adjoint representation (a "matrix large N" theory), yields a tractable large N limit. At low energies, the system consists of an overdamped boson with dynamical exponent $z=3$ coupled to a non-Fermi liquid with self energy $\Sigma(\omega) \sim \omega^{2/3}$, consistent with previous studies.