We discuss topological phenomena beyond the zero temperature equilibrium setting. We discuss the eigenstate thermalization hypothesis, which seems to forbid such phenomena, as well as the more recently discovered many-body localization, which forms a generic exception to it. We then show how to define a new quantized index for many-body-localized Floquet phases, one that is related to the GNVW index classifying quantum cellular automata (QCA) in 1 dimension.
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