Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states

TL;DR

This paper investigates the real-space effects of quenches in the SSH model, revealing conditions under which topological edge states can dynamically appear or remain hidden, depending on symmetries and initial states.

Contribution

It demonstrates how additional symmetries suppress real-space signatures of topological edge states after quenches and identifies conditions that allow their dynamical emergence.

Findings

Site occupancy remains at 1/2 after quenches due to symmetries.

Topological edge states do not appear in real-space occupancies after trivial-to-topological quenches.

Local quenches in flux-threaded rings can reveal dynamical effects of topological phases.

Abstract

The topological phase of the Su-Schrieffer-Heeger (SSH) model is known to exhibit two edge states that are topologically protected by the chiral symmetry. We demonstrate that, for any parameter quench performed on the half-filled SSH chain, the occupancy of each lattice site remains locked to $1/2$ at any time, due to the additional time-reversal and charge conjugation symmetries. In particular, for a quench from the trivial to the topological phase, no signature of the topological edge states appears in real-space occupancies, independently of the quench protocol, the temperature of the pre-quench thermal state or the presence of chiral disorder. However, a suitably designed local quench from/to a SSH ring threaded by a magnetic flux can break these additional symmetries while preserving the chiral one. Then, real-space effects of the quench do appear and exhibit different dynamical features in the topological and in the trivial phases. Moreover, when the particle filling is different from a half and the pre-quench state is not insulating, the dynamical appearance of the topological edge states is visible already in a chain, it survives time averaging and can be observed also in the presence of chiral-breaking disorder and for instantaneous quenches.