# Temporal variation in the winding number due to dynamical symmetry breaking and associated transport in a driven SSH chain

## TL;DR

This paper investigates how the winding number, a topological invariant in a driven SSH chain, varies over time under different symmetry-breaking protocols and how this affects bulk transport properties.

## Contribution

It demonstrates that the topological invariant can change when the effective Hamiltonian breaks BDI symmetry, linking symmetry breaking to transport phenomena in driven topological systems.

## Key findings

- Winding number can change under symmetry-breaking protocols.
- Bulk currents are affected by the symmetry properties of the effective Hamiltonian.
- Symmetry breaking leads to observable transport signatures in the system.

## Abstract

Considering a BDI symmetric one-dimensional SSH model, we explore the fate of the bulk topological invariant, namely, the winding number under a generic time dependent perturbation; the effective Hamiltonian, that generates the temporal evolution of the initial (ground) state of the completely symmetric initial Hamiltonian, may have the same or different symmetries. To exemplify, we consider the following protocols, namely (i) a perfectly periodic protocol (ii) a periodic protocol with noisy perturbations and also (iii) sudden changes in the parameters of the initial Hamiltonian. We establish that the topological invariant may change in some cases when the effective Hamiltonian (or the Floquet Hamiltonian in the periodic situation when observed stroboscopically) does not respect all BDI symmetries; this is manifested in the associated particle (polarisation) or heat current in the bulk. Our results establish a strong connection between the time evolution of the winding number (thus, the associated transport of currents) and the symmetry of the Hamiltonian generating the time evolution which has been illustrated considering an exhaustive set of possibilities.