# Dynamical preparation of a topological state and out of equilibrium bulk boundary correspondence in a SSH chain under periodic driving

## TL;DR

This paper demonstrates how periodic driving can dynamically prepare and control topological states in SSH chains, revealing a non-equilibrium bulk-boundary correspondence and enabling the creation of out-of-equilibrium topological insulators.

## Contribution

It introduces a method to induce and restore topological phases in SSH chains via adiabatic periodic driving, establishing a non-equilibrium bulk-boundary correspondence.

## Key findings

- Successfully prepared a stroboscopic topological state from a trivial one.
- Observed topologically protected edge states in a long open chain.
- Dynamically created higher winding phases in extended SSH chains.

## Abstract

Exploiting the possibility of temporal variation of the winding number, we have prepared a SSH chain in its {\it stroboscopic} topological state, starting from the trivial one, by application of a periodic perturbation. The periodic driving, we employ here, is adiabatically switched on to break the particle-hole symmetry and generate a chiral mass term in the effective Floquet Hamiltonian; consequently the Floquet Hamiltonian also gets deformed without crossing the gapless quantum critical point. The particle hole symmetry is subsequently restored in the Floquet Hamiltonian by adiabatically switching off a part of the periodic potential. Thereafter, the Floquet Hamiltonian develops a symmetry protected non-trivial topological winding number. Furthermore, we also observe stroboscopic topologically protected localised edge states in a long open chain and show that a bulk boundary correspondence survives a unitary non-equilibrium situation in 1D BDI Hamiltonians. Moreover, considering an extended SSH chain with higher neighbour hoppings, we dynamically prepare the system in a stroboscopic out-of-equilibrium topological insulator state starting from a metallic regime. At the same time, we establish the dynamical preparation of higher winding phases in an extended SSH chain with stroboscopic bulk-boundary correspondence in the non-equilibrium state of the system.