Title: Topology of quantum systems out of equilibrium

Speaker: Max McGinley (University of Cambridge)

Abstract: Topological phases of matter have attracted a huge amount of interest in recent years, thanks largely to the discovery of topological insulators in two and three spatial dimensions, amongst other experimental successes. These phases fall outside of Landau’s symmetry-breaking paradigm, and can be understood through some notion of a `twist’ in the ground state wavefunction, partnered with characteristic gapless edge states at their physical boundaries. Through understanding the mathematical structures which encode the ground state wavefunction’s topological properties, it has been possible to exhaustively classify different topological phases in a manner which is sensitive to spatial dimension, symmetries, and the presence/absence of interactions. In this talk, rather than discussing the topological properties of ground states of Hamiltonians, I will consider nonequilibrium states resulting from unitary time evolution. I will demonstrate how the topology of wavefunctions can differ in and out of equilibrium, and provide some simple concrete examples which demonstrate their key phenomenology. Just as in equilibrium, it is possible to construct an exhaustive non-equilibrium classification of topological systems, and I will present this classification for non-interacting fermions with non-spatial symmetries, encompassing the majority of the so-far experimentally realized systems. I will conclude by discussing the direct experimental consequences of our results, including important ramifications for the use of topological zero-energy bound states in quantum information technologies.

Time: Thursday, 11 April 2019, 2:30 pm

Location: Lecture Room, 1st Floor, School of Theoretical Physics, DIAS, 10 Burlington Road, Dublin 4