Area laws in a many-body localized state and its implications for topological order

TL;DR

This paper investigates many-body localization in disordered interacting systems, demonstrating an area law for entanglement entropy in most states, and explores its implications for stabilizing topological order and quantum memories.

Contribution

It provides numerical evidence for area law entanglement in many-body localized states and discusses how localization can support topological order at finite energy density.

Findings

Most states exhibit an area law for entanglement entropy.

Rare states show higher entanglement, deviating from the typical behavior.

Localization can potentially stabilize topological order at non-zero energy density.

Abstract

The question whether Anderson insulators can persist to finite-strength interactions - a scenario dubbed many-body localization - has recently received a great deal of interest. The origin of such a many-body localized phase has been described as localization in Fock space, a picture we examine numerically. We then formulate a precise sense in which a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator. We call such a state a many-body localized state and define a many-body localized phase as one in which almost all states are many-body localized states. We explore the possible consequences of this; the most striking is an area law for the entanglement entropy of almost all excited states in a many-body localized phase. We present the results of numerical calculations for a one-dimensional system of spinless fermions. Our results are consistent with an area law and, by implication, many-body localization for almost all states and almost all regions for weak enough interactions and strong disorder. However, there are rare regions and rare states with much larger entanglement entropies. Furthermore, we study the implications that many-body localization may have for topological phases and self-correcting quantum memories. We find that there are scenarios in which many-body localization can help to stabilize topological order at non-zero energy density, and we propose potentially useful criteria to confirm these scenarios.