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

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.

Expanded version; 11 pages, 6 figures

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• Dissipative preparation of many-body Floquet Chern insulators
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Anomalous Josephson effect and rectification in junctions between Floquet topological superconductors
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
• Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases
• Universal Landau-Zener regimes in dynamical topological phase transitions
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor