Almost-conserved operators in nearly many-body localized systems

TL;DR

This paper constructs and analyzes almost conserved local operators in a disordered spin chain near the many-body localization transition, revealing insights into slow dynamics and Griffiths effects.

Contribution

It introduces a method to identify and study almost conserved operators, linking their properties to the system's phase transition and dynamical behavior.

Findings

Scaling of commutators indicates Griffiths effects and localization transition

Distribution tails distinguish diffusive and sub-diffusive dynamics

Extreme value theory characterizes the probability of slow operators

Abstract

We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and sub-diffusive dynamics in the thermal phase.