Slow scrambling in disordered quantum systems

TL;DR

The paper investigates how static disorder affects scrambling in quantum many-body systems by analyzing the growth of local operators through out-of-time-ordered correlators. Using both non-interacting disordered models and a standard many-body localization fixed-point Hamiltonian, it demonstrates that disorder generally slows scrambling and, in the MBL phase, drives a slow logarithmic growth of the operator radius $R_W(t)$. In contrast, introducing weak interactions in a diffusive metal leads to ballistic operator growth with $R_W(t) \sim v_B t$ and a butterfly velocity $v_B$ scaling as $v_B \sim \sqrt{D \Gamma}$, where $D$ is the diffusion constant and $\Gamma$ the inelastic scattering rate. These results link scrambling dynamics to entanglement growth and offer experimental avenues to probe localization and transitions via OTO measurements, highlighting a nuanced interplay between disorder and interactions in information spreading.

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.