Slow scrambling in disordered quantum systems

TL;DR

This paper investigates how static disorder affects quantum information scrambling, showing that disorder generally slows or halts scrambling, especially in many-body localized states, with implications for understanding quantum chaos.

Contribution

It demonstrates that static disorder slows or stops scrambling in quantum systems, including the characterization of many-body localization effects on operator growth.

Findings

Disorder delays the onset of scrambling.

Many-body localized states exhibit logarithmic operator growth.

Weak interactions may alter commutator growth in diffusive metals.

Abstract

Recent work has studied the growth of commutators as a probe of chaos and information scrambling in quantum many-body systems. In this work we study the effect of static disorder on the growth of commutators in a variety of contexts. We find generically that disorder slows the onset of scrambling, and, in the case of a many-body localized state, partially halts it. We access the many-body localized state using a standard fixed point Hamiltonian, and we show that operators exhibit slow logarithmic growth under time evolution. We compare the result with the expected growth of commutators in both localized and delocalized non-interacting disordered models. Finally, based on a scaling argument, we state a conjecture about the effect of weak interactions on the growth of commutators in an interacting diffusive metal.