Classification of topological insulators and superconductors out of equilibrium

We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium-it is robust against disorder and interactions, and exhibits a nonequilibrium bulk-boundary correspondence, which connects bulk topological properties to the entanglement spectrum. We explicitly construct a nonequilibrium classification of noninteracting fermionic systems with nonspatial symmetries in all spatial dimensions (the 'tenfold way'), which differs from its equilibrium counterpart. Direct physical consequences of our classification are discussed, including important ramifications for the use of topological zero-energy bound states in quantum information technologies.