Local conservation laws and the structure of the many-body localized states

TL;DR

This paper constructs a complete set of local integrals of motion to characterize the many-body localized phase, providing insights into its structure and implications for non-equilibrium dynamics and coherence preservation.

Contribution

It introduces a method to explicitly construct local integrals of motion in the MBL phase, advancing understanding of its eigenstate structure and dynamical properties.

Findings

Local perturbations act locally on eigenstates in MBL phase

Numerical simulations support the local action assumption

MBL phase can protect quantum coherence

Abstract

We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its non-equilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.