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The question whether Anderson insulators can persist to finite-strength interactions - a scenario dubbed many-body localization - has received a great deal of interest. We 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, and define a many-body localized phase based on this. 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. Furthermore, we study the implications that many-body localization may have for topological phases and identify scenarios in which many-body localization can help to stabilize topological order at non-zero energy density. We also explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time-evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed.

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Bela Bauer, Microsoft Station Q
Seminar Room, Conainer Building
Contact: Simon Trebst