Quantum Electrodynamics in 2+1 Dimensions With Quenched Disorder: Quantum Critical States With Interactions and Disorder

Abstract

Quantum electrodynamics in 2+1 dimensions (QED3) 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 QED3 in the presence of weak quenched disorder in its two spatial directions. When the disorder explicitly breaks the fermion flavor symmetry from SU(2N) → U(1) × SU(N) but preserves time-reversal symmetry, we find that the theory flows to a nontrivial fixed line at nonzero 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.