Chiral symmetry and bulk{boundary correspondence in periodically driven one-dimensional systems

By J. Asbóth, B. Tarasinski, P. Delplace. 2014

190 citations recorded by the source corpus.

In periodically driven lattice systems, the effective (Floquet) Hamiltonian can be engineered to be topological; then, the principle of bulk-boundary correspondence guarantees the existence of robust edge states. However, such setups can also host edge states not predicted by the Floquet Hamiltonian. The exploration of such edge states and the corresponding unique bulk topological invariants has only recently begun. In this work we calculate these invariants for chiral symmetric periodically driven one-dimensional systems. We find simple closed expressions for these invariants, as winding numbers of blocks of the unitary operator corresponding to a part of the time evolution. This gives a robust way to tune these invariants using sublattice shifts. We illustrate our ideas on the periodically driven Su-Schrieffer-Heeger model, which, as we show, can realize a discrete-time quantum walk; this opens a useful connection between periodically driven lattice systems and discrete-time quantum walks. Our work helps interpret the results of recent simulations where a large number of Floquet Majorana fermions in periodically driven superconductors have been found.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/23c1d96ce3297a4328ba37fb25d27ab162d07501

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Floquet topological transitions in a driven one-dimensional topological insulator (2015, background): “Although previous works have addressed driven one-dimensional systems in a variety of contexts [11,24,31,44], the above question still remains.”
Topological bands for ultracold atoms (2018, unknown): “…stable edge modes at quasi-energies 45 = ~ω/2 have been theoretically demonstrated in periodically driven lattices models with sublattice (chiral) symmetry analogous to the SSH model (Asbóth et al., 2014), and in Floquet superfluid systems where they appear as Majorana modes (Jiang et al., 2011).”
Periodic table for Floquet topological insulators (2016, background): “We note that our definition of chiral symmetry for periodic systems is slightly different from that used in some previous works [34, 36].”
Classification of Interacting Topological Floquet Phases in One Dimension (2016, methodology): “[31] C. Interacting fermionic Floquet SPTs The presence of a global symmetry group, G, constrains the possible form of perturbations (i.e. restricts the entries of M (0,π)), and can protect multiple MZM and MPMs.”