Dynamics of quantum information in many-body localized systems

TL;DR

This paper investigates how quantum information spreads in disordered many-body systems, revealing distinct behaviors in thermalizing, Anderson localized, and many-body localized phases, and proposes MPO truncation errors as a potential critical point diagnostic.

Contribution

It provides a comprehensive analysis of quantum information dynamics across different localization regimes using multiple computational methods.

Findings

Remnant information distinguishes localized from thermal phases.

Mutual information propagation varies with system phase.

MPO truncation errors fluctuate near the localization transition.

Abstract

We characterize the information dynamics of strongly disordered systems using a combination of analytics, exact diagonalization, and matrix product operator simulations. More specifically, we study the spreading of quantum information in three different scenarios: thermalizing, Anderson localized, and many-body localized. We qualitatively distinguish these cases by quantifying the amount of remnant information in a local region. The nature of the dynamics is further explored by computing the propagation of mutual information with respect to varying partitions. Finally, we demonstrate that classical simulability, as captured by the magnitude of MPO truncation errors, exhibits enhanced fluctuations near the localization transition, suggesting the possibility of its use as a diagnostic of the critical point.