The renormalization group in quantum quenched disorder

Abstract

We study the renormalization group flow in general quantum field theories with quenched disorder, focusing on random quantum critical points. We show that in disorder-averaged correlation functions the flow mixes local and non-local operators. This leads to a new crossover exponent related to the disorder (as in classical disorder). We show that the time coordinate is rescaled at each RG step, leading to Lifshitz scaling at critical points. We write a universal formula for the dynamical scaling exponent z for weak disorder.