Unbounded growth of entanglement in models of many-body localization

TL;DR

This paper investigates whether many-body localized quantum systems can exhibit unbounded entanglement growth, revealing that interactions cause entanglement to grow indefinitely even in localized phases, challenging previous assumptions.

Contribution

It demonstrates through numerical analysis that interactions lead to unbounded entanglement growth in many-body localized systems, contrary to prior expectations of localization.

Findings

Entanglement grows without limit in localized phases due to interactions.

Local measurements reveal large, nonthermal entropy in the system.

Entanglement growth is approximately logarithmic over diverging timescales.

Abstract

An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of interacting spinless fermions in one dimension described by the random-field XXZ Hamiltonian. Interactions induce a dramatic change in the propagation of entanglement and a smaller change in the propagation of particles. For even weak interactions, when the system is thought to be in a many-body localized phase, entanglement shows neither localized nor diffusive behavior but grows without limit in an infinite system: interactions act as a singular perturbation on the localized state with no interactions. The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state. This entropy develops slowly (approximately logarithmically) over a diverging time scale as in glassy systems.