Scrambling dynamics across a thermalization-localization quantum phase transition

TL;DR

This paper investigates how quantum information scrambling changes across a transition from thermalization to localization in disordered spin chains, revealing a sharp change in operator growth behavior.

Contribution

It provides the first detailed analysis of operator growth dynamics across the thermalization-localization transition using matrix product operator methods.

Findings

Ballistic operator growth at weak disorder

Sharp transition to sub-ballistic spreading

Transition point below the many-body localization threshold

Abstract

We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the transition from sub-ballistic to logarithmic behavior at the actual eigenstate localization transition is not resolved in our finite numerics. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.