A critical fixed point of QED$_3$ with quenched disorder

Quantum electrodynamics in 2+1-dimensions (QED$_3$) describes a critical phase of matter known as the algebraic spin liquid. It is a strongly coupled conformal field theory with a U(1) gauge boson coupled to 4$N_f$ two-component massless fermions. At $N_f=1$, this is a proposed ground state of the spin-1/2 kagome Heisenberg antiferromagnet. We study the behaviour of QED$_3$ in the presence of weak quenched disorder in its two spatial directions. When the disorder explicitly breaks the fermion flavour symmetry from SU($4N_f$)$\rightarrow$U(1)$\times$SU($2N_f$), we find that the theory flows to a non-trivial critical point with a dynamical critical exponent $z>1$. At this critical point, we determine the zero-temperature spin conductivity. Our calculations are done in the large-$N_f$ limit and the disorder is handled using the replica method.