Renormalization group in quantum critical theories with Harris-marginal disorder

TL;DR

This paper develops a renormalization group framework for weak Harris-marginal disorder in strongly interacting quantum critical theories with emergent conformal invariance, revealing flow towards universal fixed points and confirming predictions via holography.

Contribution

It introduces a one-loop renormalization group analysis for Harris-marginal disorder in quantum critical theories with conformal invariance, connecting field theory and holographic results.

Findings

Disorder flows towards universal fixed points.

Holographic models agree with the renormalization group predictions.

The approach is most effective with few low-dimension operators.

Abstract

We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue that previously proposed random lines of fixed points with Lifshitz scaling in fact flow towards other universal fixed points, and this flow is captured by a "one-loop" analysis. Our approach appears best controlled in theories with only a few operators with low scaling dimension. In this regime, we compare our predictions for the flow of disorder to holographic models, and find complete agreement.