# QED$_3$ with quenched disorder: quantum critical states with interactions and disorder

## TL;DR

This paper investigates how weak quenched disorder affects the quantum electrodynamics in 2+1 dimensions (QED$_3$), revealing a non-trivial fixed line with a varying dynamical critical exponent and calculating the zero-temperature flavor conductivity.

## Contribution

It introduces a large-$N$ analysis of disordered QED$_3$, showing the emergence of a fixed line with a continuously varying critical exponent under specific symmetry-breaking conditions.

## Key findings

- Disorder induces a non-trivial fixed line in QED$_3$.
- The dynamical critical exponent $z$ varies continuously along the fixed line.
- Zero-temperature flavor conductivity is computed at the critical line.

## Abstract

Quantum electrodynamics in 2+1-dimensions (QED$_3$) is a strongly coupled conformal field theory (CFT) of a U(1) gauge field coupled to $2N$ two-component massless fermions. The $N=2$ CFT has been proposed as a ground state of the spin-1/2 kagome Heisenberg antiferromagnet. We study QED$_3$ in the presence of weak quenched disorder in its two spatial directions. When the disorder explicitly breaks the fermion flavor symmetry from SU($2N$)$\rightarrow$U(1)$\times$SU($N$) but preserves time-reversal symmetry, we find that the theory flows to a non-trivial fixed line at non-zero disorder with a continuously varying dynamical critical exponent $z>1$. We determine the zero-temperature flavor (spin) conductivity along the critical line. Our calculations are performed in the large-$N$ limit, and the disorder is handled using the replica method.