Quantum quench dynamics in topological systems

Can quench dynamics involving the dynamic tuning of a parameter in a system, such as a magnetic field, act as a probe of topological phases? Can the existence of topological order lead to a different realm in non-equilibrium dynamics? In this talk, I will address these two questions in the context of two hallmarks of topological phases – ground state degeneracies and the presence of edge modes. In the instance of quenching across a critical point separating a topological and a trivial phase, I will argue that under certain conditions, ground state degeneracies result in a ‘topological blocking’ phenomena. In such a situation, topological constraints force the system to completely occupy the excited spectrum of the final state and to have zero overlap with the final ground state. I will then describe the effect of edge modes on quenches in the paradigm Majorana wire system whose ends are expected to carry Majorana fermionic bound modes. Here, parity switches associated with the bound modes drastically affect non-equilibrium quench dynamics. In these contexts, I will discuss possible influences of disorder on topologically constrained non-equilibrium dynamics. Finally, I will propose that quantum Hall systems can behave as gravitational analogs and will explore potential simulations of black hole dynamics in these systems.