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

Understand

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.