A phenomenology of certain many-body-localized systems

TL;DR

This paper explores the properties of many-body localized quantum systems, defining their integrability, localized conserved quantities, and analyzing entanglement spreading, highlighting their potential for quantum information recovery.

Contribution

It introduces a framework for identifying localized conserved operators and discusses their role in the integrability and entanglement dynamics of many-body localized systems.

Findings

Localized conserved operators can be identified as interacting pseudospins.

Quantum states of these pseudospins are recoverable via echo procedures.

Entanglement spreads through dephasing among localized conserved operators.

Abstract

We consider isolated quantum systems with all of their many-body eigenstates localized. We define a sense in which such systems are integrable, and discuss a method for finding their localized conserved quantum numbers ("constants of motion"). These localized operators are interacting pseudospins and are subject to dephasing but not to dissipation, so any quantum states of these pseudospins can in principle be recovered via (spin) echo procedures. We also discuss the spreading of entanglement in many-body localized systems, which is another aspect of the dephasing due to interactions between these localized conserved operators.