Dynamical preparation of a topological state and out-of-equilibrium bulk-boundary correspondence in a Su-Schrieffer-Heeger chain under periodic driving

Abstract

Exploiting the possibility of temporal variation of the winding number, we have prepared a Su-Schrieffer-Heeger (SSH) chain in its 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 nontrivial topological winding number. Furthermore, we also observe stroboscopic topologically protected localized edge states in a long open chain and show that a bulk-boundary correspondence survives a unitary nonequilibrium situation in one-dimensional BDI Hamiltonians. Moreover, considering an extended SSH chain with higher neighbor 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 nonequilibrium state of the system.