Efficient computation of the $W_3$ topological invariant and application to Floquet-Bloch systems

Abstract

We introduce an efficient algorithm for the computation of the $W_3$ invariant of general unitary maps, which converges rapidly even on coarse discretization grids. The algorithm does not require extensive manipulation of the unitary maps, identification of the precise positions of degeneracy points, or fixing the gauge of eigenvectors. After construction of the general algorithm, we explain its application to the $2+1$ dimensional maps that arise in the Floquet-Bloch theory of periodically driven two-dimensional quantum systems. We demonstrate this application by computing the $W_3$ invariant for an irradiated graphene model with a continuously modulated Hamilton operator, where it predicts the number of anomalous edge states in each gap.

16 pages, 8 figures. Version as published

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Cited by in corpus (12)

• Non-Hermitian Boundary State Engineering in Anomalous Floquet Topological Insulators
• Fermionic time-reversal symmetry in a photonic topological insulator
• Effective Floquet Hamiltonian in the low-frequency regime
• Topological origin of quantized transport in non-Hermitian Floquet chains
• Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry
• Universal driving protocol for symmetry-protected Floquet topological phases
• Dynamical characterization of Weyl nodes in Floquet Weyl semimetal phases
• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
• Driven Hofstadter Butterflies and Related Topological Invariants
• Dimensional reduction and scattering formulation for even topological invariants
• Eigenvalue crossings in Floquet topological systems
• Real and imaginary edge states in stacked Floquet honeycomb lattices