Anomalous Boundary Modes in a Floquet Hyperbolic System

• URL: http://arxiv.org/abs/2607.28719v1
• Date: Thu, 30 Jul 2026 18:00:01 GMT
• Title: Anomalous Boundary Modes in a Floquet Hyperbolic System
• Abstract summary: We construct an anomalous Floquet topological phase on a negatively curved hyperbolic lattice.<n>We map the bulk $0$ and $$ quasienergy gaps and identify the gapped regions connected to the trivial and anomalous open-boundary spectra.<n>We introduce a small-boundary spectral-flow diagnostic based on punctured periodic hyperbolic lattices.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We construct an anomalous Floquet topological phase on a negatively curved hyperbolic lattice. The model is a tight-binding Hamiltonian with a periodically repeated four-color edge-hopping sequence and a sublattice-staggered onsite potential step. The topological regime is reached near the limit in which a single hopping step transfers amplitude completely across an active edge, while the trivial regime is reached near the point where two full hops occur along an active edge during a single hopping step, returning the amplitude to its starting site. In finite open patches, the topological regime is characterized by bulk quasienergy gaps at $0$ and $π$ that are populated by in-gap states, in contrast to a trivial regime where these gaps remain empty. Using compact periodic lattices, we map the bulk $0$ and $π$ quasienergy gaps and identify the gapped regions connected to the trivial and anomalous open-boundary spectra. We diagnose the in-gap states as chiral boundary modes by their real-space dynamics. Finally, we introduce a small-boundary spectral-flow diagnostic based on punctured periodic hyperbolic lattices, which avoids the ambiguity associated with the extensive outer boundary of finite hyperbolic patches. This puncture-based diagnostic should be useful for studying other topological hyperbolic systems.

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