Unbounded Growth of Entanglement in Models of Many-Body Localization

TLDR

Whether disorder can localize a closed quantum system of interacting particles remains an open question. The authors numerically evolve unentangled initial states of one‑dimensional spinless fermions governed by a random‑field XXZ Hamiltonian. Even weak interactions cause entanglement to grow unboundedly (logarithmically) in the many‑body localized phase, producing large nonthermal entropy that evolves slowly over diverging timescales, while particle transport changes only modestly.

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.