Boundary-induced dynamics in 1D topological systems and memory effects of edge modes

TL;DR

This paper investigates how changing boundary conditions in 1D topological systems like the Kitaev chain and SSH model induces rate-dependent dynamics and memory effects, highlighting the role of topology in these phenomena.

Contribution

It demonstrates that boundary-induced dynamics and memory effects are specific to topological phases, contrasting with non-topological regimes where such effects are absent.

Findings

Steady-state edge mode density depends on boundary change rate

Correlation functions can retain memory of initial conditions across broken links

Memory effects are absent in non-topological regimes

Abstract

Dynamics induced by a change of boundary conditions reveals rate-dependent signatures associated with topological properties in one-dimensional Kitaev chain and SSH model. While the perturbation from a change of the boundary propagates into the bulk, the density of topological edge modes in the case of transforming to open boundary condition reaches steady states. The steady-state density depends on the transformation rate of the boundary and serves as an illustration of quantum memory effects in topological systems. Moreover, while a link is physically broken as the boundary condition changes, some correlation functions can remain finite across the broken link and keep a record of the initial condition. By testing those phenomena in the non-topological regimes of the two models, none of the interesting signatures of memory effects can be observed. Our results thus contrast the importance of topological properties in boundary-induced dynamics.