Freezing topological edge states after a quantum quench

Topological edge states are tell-tale signs of the non-trivial winding of wavefunctions found in topological materials. Here we argue that characteristics of such topological edge states (e.g., probability density, pseudospin density) that are prepared in a topologically non-trivial hamiltonian persist even when the hamiltonian is quenched into a trivial phase. For instance, we find that the probability density of 1D domain wall topological edge states can appear "frozen" over a long time window even after the hamiltonian is quenched into a trivial gapped phase maintaining a well-defined peaked spatial profile. After this "frozen" window, the topological boundary mode decays slowly. This behavior highlights the unusual features of nonequilibrium protocols enabling quenches to dynamically control spatially confined topological edge states in quantum quenches. 

This work was supported by Singapore MOE Academic Research Fund Tier 3 Grant MOE2018-T3-1-002 and the Singapore National Research Foundation (NRF) under NRF fellowship award NRF-NRFF 2016-05.