Topological phase transitions in finite-size periodically driven translationally invariant systems

Abstract

It is known that, in the thermodynamic limit, the Chern number of a translationally invariant system cannot change under unitary time evolutions that are smooth in momentum space. Yet a real-space counterpart of the Chern number, the Bott index, has been shown to change in periodically driven systems with open boundary conditions. Here we prove that the Bott index and the Chern number are identical in translationally invariant systems in the thermodynamic limit. Using the Bott index, we show that, in finite-size translationally invariant systems, a Fermi sea under a periodic drive that is turned on slowly can acquire a different topology from that of the initial state. This can happen provided that the gap-closing points in the thermodynamic limit are absent in the discrete Brillouin zone of the finite system. Hence, in such systems, a periodic drive can be used to dynamically prepare topologically nontrivial states starting from topologically trivial ones.

8 pages, 4 figures. Updated to published version with the addition of Ref [32]. Typo fix

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• Periodically-driven facilitated high-efficiency dissipative entanglement with Rydberg atoms
• Driven quantum many-body systems and out-of-equilibrium topology
• Bulk Spectrum and K-theory for Infinite-Area Topological Quasicrystal
• Time-dependent topological systems: A study of the Bott index
• Floquet topological transitions in extended Kane-Mele models with disorder
• Charge excitations across a superconductor-insulator transition
• Real-time dynamics of the photoinduced topological state in organic conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ under continuous-wave and pulse excitations
• Scheme to Equilibrate the Quantized Hall Response of Topological Systems from Coherent Dynamics
• Universal Landau-Zener regimes in dynamical topological phase transitions
• Self-consistent study of topological superconductivity in two-dimensional quasicrystals
• Topology in the space-time scaling limit of quantum dynamics
• The Bott index of two unitary operators and the integer quantum Hall effect