Stability and quasi-Periodicity of Many-Body Localized Dynamics

TL;DR

This paper demonstrates that many-body localized systems exhibit stable, quasi-periodic entanglement dynamics in the thermodynamic limit, providing a new criterion to distinguish MBL from thermalizing phases and challenging previous logarithmic growth observations.

Contribution

It introduces a novel characterization of MBL through persistent quasi-periodic entanglement dynamics, supported by perturbation theory and modeling of rare regions.

Findings

Entanglement in MBL systems remains quasi-periodic at large scales.

Logarithmic entanglement growth is due to statistical averaging, not intrinsic dynamics.

MBL stability is confirmed in disordered Heisenberg chains.

Abstract

The connection between entanglement dynamics and non-equilibrium statistics in isolated many-body quantum systems has been established both theoretically and experimentally. Many-Body Localization (MBL), a phenomenon where interacting particles in disordered (i.e., random) chains fail to thermalize, exemplifies this connection. However, the systematic proof of critical phenomena such as MBL remains challenging due to the lack of robust methods for analyzing many-body entanglement dynamics. In this paper, we identify MBL through quasi-periodic dynamics in the entanglement evolution of subsystems in a disordered Heisenberg chain. This new form of characterizing MBL, through stable quasi-periodic dynamics of entanglement -- where stable means they persist in the thermodynamic limit -- concretely distinguishes between two competing scenarios: fully localized behavior of subsystems or slowly, exponentially slow in disorder, thermalizing subsystems -- a heated controversy in the literature. Utilizing perturbation theory, we derive the entanglement dynamics of single spins through an infinite perturbative series, while also modeling rare Griffiths regions (locally thermal inclusions). Our results prove that in regimes of sufficiently strong disorder, the entanglement evolution of individual subsystems remains quasi-periodic in the thermodynamic limit, thereby providing concrete evidence for the stability of MBL dynamics in disordered Heisenberg chains. This behavior contrasts with the widely reported logarithmic growth of subsystem entanglement in the MBL phase. We show that the logarithmic growth observed in prior studies arises from statistical ensemble averaging, which is prohibited due to the intrinsic non-ergodic dynamics characteristic of MBL systems, rooted in their quasi-periodic features.