Topology of Quantum Systems Out of Equilibrium*

We investigate the topological properties of many-body quantum systems undergoing unitary time-evolution. We find that it is possible for the topology of the wavefunction to change out of equilibrium, and accordingly establish the existence of a robust nonequilibrium topological classification which generally differs from equilibrium [1]. The classification naturally inherits phenomenology familiar from equilibrium – it is robust against disorder and interactions, and exhibits a nonequilibrium bulk-boundary correspondence, which we probe using the entanglement spectrum. We explicitly construct a nonequilibrium generalisation of the `ten-fold way', which applies to non-interacting fermionic systems with non-spatial symmetries in all dimensions [2]. The differences between equilibrium and nonequilibrium topology are shown to have directly observable consequences, in both bulk and boundary physics. In particular, we show that non-equilibrium topological effects have important ramifications for various Majorana fermion-based implementations of quantum memories.

[1] Max McGinley, Nigel Cooper, PRL 121 090401 (2018)
[2] Max McGinley, Nigel Cooper (to appear)