Influence of dephasing on many-body localization

TL;DR

This paper investigates how dephasing noise impacts many-body localization in a disordered XXZ spin chain, revealing that while purity and entropy suggest delocalization, operator space entanglement indicates persistent localized dynamics.

Contribution

It introduces a Markovian framework for understanding dephasing effects on many-body localized systems and identifies a scaling variable independent of interaction strength.

Findings

Purity and von Neumann entropy are extensive and show no localization signatures.

Operator space entanglement entropy grows logarithmically before saturation.

Relaxation dynamics are governed by a bond-disordered Markov process.

Abstract

We study the effects of dephasing noise on a prototypical many-body localized system -- the XXZ spin 1/2 chain with a disordered magnetic field. At times longer than the inverse dephasing strength the dynamics of the system is described by a probabilistic Markov process on the space of diagonal density matrices, while all off-diagonal elements of the density matrix decay to zero. The generator of the Markovian process is a bond-disordered spin chain. The scaling variable is identified, and independence of relaxation on the interaction strength is demonstrated. We show that purity and von Neumann entropy are extensive, showing no signatures of localization, while the operator space entanglement entropy exhibits a logarithmic growth with time until the final saturation corresponding to localization breakdown, suggesting a many-body localized dynamics of the effective Markov process.