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This research constructs an anomalous Floquet topological phase on a negatively curved hyperbolic lattice using tight-binding Hamiltonians with periodic hopping sequences. The study identifies chiral boundary modes within bulk quasienergy gaps at 0 and $\pi$, introducing a novel puncture-based diagnostic to analyze spectral flow without ambiguity from extensive outer boundaries. These findings advance the theoretical understanding of topological phases in non-Euclidean geometries, which is relevant for future quantum simulation architectures.
Anomalous Boundary Modes in a Floquet Hyperbolic System
arXiv:2607.28719v1 Announce Type: cross 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 $\pi$ 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 $\pi$ 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.
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 $\pi$ 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 $\pi$ 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.
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)
arXiv:2607.28719 [cond-mat.mes-hall]
(or arXiv:2607.28719v1 [cond-mat.mes-hall] for this version)
https://doi.org/10.48550/arXiv.2607.28719 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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