# Quench dynamics of edge states in a finite extended Su-Schrieffer-Heeger system

## TL;DR

This paper investigates how different quench paths between topological phases in an extended SSH model affect edge state survival and transport properties, revealing path-dependent dynamics and velocities.

## Contribution

It introduces a detailed analysis of winding number transition paths and their impact on edge state dynamics and transport in a long-range hopping SSH model.

## Key findings

- Edge state survival probability depends on the winding number transition path.
- Transport velocities vary with the winding number transition path.
- Path-dependent energy band and edge state structures explain velocity variations.

## Abstract

We examine the quench dynamics of an extended Su-Schrieffer-Heeger(SSH) model involving long-range hopping that can hold multiple topological phases. Using winding number diagrams to characterize the system's topological phases geometrically, it is shown that there can be multiple winding number transition paths for a quench between two topological phases. The dependence of the quench dynamics is studied in terms of the survival probability of the fermionic edge modes and post-quench transport. For two quench paths between two topological regimes with the same initial and final topological phase, the survival probability of edge states is shown to be strongly dependent on the winding number transition path. This dependence is explained using energy band diagrams corresponding to the paths. Following this, the effect of the winding number transition path on transport is investigated. We find that the velocities of maximum transport channels varied along the winding number transition path. This variation depends on the path we choose, i.e., it increases or decreases depending upon the path. An analysis of the coefficient maps, energy spectrum, and spatial structure of the edge states of the final quench Hamiltonian provides an understanding of the path-dependent velocity variation phenomenon.