Many-body localization under the microscope

The high-energy dynamics of quantum many-body systems are usually governed by their approach towards thermal equilibrium, which rapidly simplifies their local behavior to the framework of classical statistical mechanics. A breakdown of this paradigm can occur in the presence of disorder, where many-body localization completely inhibits those thermalization dynamics. Strikingly, despite their localized nature, many-body-localized systems are expected to show ongoing coherent dynamics that manifest as a slow buildup of entanglement.
 
In my talk, I will present our recent studies on many-body localization. We prepare a pure quantum state out of equilibrium, evolve it unitarily under the interacting Aubry-André Hamiltonian, and perform projective measurements in the Fock basis. We observe a number of key properties, such as the mentioned slow buildup of entanglement, extensive entanglement of the many-body state, and a diverging state complexity at the many-body localization transition.