Scrambling and thermalization in a diffusive quantum many-body system

TL;DR

This paper investigates how information scrambles in a diffusive quantum many-body system, revealing that while global thermalization is slow and diffusive, quantum information spreads ballistically, using advanced numerical methods and proposing experimental protocols.

Contribution

It demonstrates the ballistic spreading of OTO correlators in a diffusive, incoherent quantum system and introduces a feasible experimental protocol to measure these correlations.

Findings

OTOC correlators spread ballistically despite diffusive transport of conserved quantities

Global thermalization occurs via slow, diffusive processes

Proposed experimental protocol enables measurement of OTO and time-ordered correlators

Abstract

Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined quasi-particles. Thus far, it is largely elusive how OTO correlators spread in incoherent systems with diffusive transport governed by a few globally conserved quantities. Here, we study the dynamical response of such a system using high-performance matrix-product-operator techniques. Specifically, we consider the non-integrable, one-dimensional Bose-Hubbard model in the incoherent high-temperature regime. Our system exhibits diffusive dynamics in time-ordered correlators of globally conserved quantities, whereas OTO correlators display a ballistic, light-cone spreading of quantum information. The slowest process in the global thermalization of the system is thus diffusive, yet information spreading is not inhibited by such slow dynamics. We furthermore develop an experimentally feasible protocol to overcome some challenges faced by existing proposals and to probe time-ordered and OTO correlation functions. Our study opens new avenues for both the theoretical and experimental exploration of thermalization and information scrambling dynamics.