# The renormalization group in quantum quenched disorder

## TL;DR

This paper investigates the renormalization group flow in quantum field theories with quenched disorder, revealing how disorder affects scaling behavior and introduces a new crossover exponent, with implications for quantum critical points.

## Contribution

It introduces a universal formula for the dynamical scaling exponent z in disordered quantum systems and analyzes the mixing of operators under RG flow.

## Key findings

- Disorder-averaged correlation functions exhibit mixing of local and non-local operators.
- A new crossover exponent related to disorder is identified.
- Lifshitz scaling emerges at quantum critical points with 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.