Phenomenology of fully many-body-localized systems

TL;DR

This paper explores the properties of fully many-body localized systems, highlighting their integrability, localized conserved operators, and the dynamics of entanglement and length scales near the phase transition.

Contribution

It introduces a framework for understanding fully many-body localized systems as integrable with localized conserved operators and analyzes their entanglement dynamics and phase transition behavior.

Findings

Localized conserved operators can be represented as interacting pseudospins.

Unitary evolution causes dephasing without pseudospin flips, enabling echo recovery.

Multiple length scales exist, with some diverging at the phase transition.

Abstract

We consider fully many-body localized systems, i.e. isolated quantum systems where all the many-body eigenstates of the Hamiltonian are localized. We define a sense in which such systems are integrable, with localized conserved operators. These localized operators are interacting pseudospins, and the Hamiltonian is such that unitary time evolution produces dephasing but not "flips" of these pseudospins. As a result, an initial quantum state of a pseudospin can in principle be recovered via (pseudospin) echo procedures. We discuss how the exponentially decaying interactions between pseudospins lead to logarithmic-in-time spreading of entanglement starting from nonentangled initial states. These systems exhibit multiple different length scales that can be defined from exponential functions of distance; we suggest that some of these decay lengths diverge at the phase transition out of the fully many-body localized phase while others remain finite.