-Continuum limit of bipartite lattices - The SSH model

• URL: http://arxiv.org/abs/2509.11900v2
• Date: Sat, 08 Nov 2025 11:05:12 GMT
• Title: -Continuum limit of bipartite lattices - The SSH model
• Authors: Fotios K. Diakonos, P. Schmelcher,
• Abstract summary: We present a continuous non-local model that faithfully replicates the rich topological and spectral features of the Su-Schrieffer-Heeger (SSH) model.<n>Our method lays the foundation for constructing non-local, continuous analogues of a wide class of bipartite and multipartite lattices.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a continuous non-local model that faithfully replicates the rich topological and spectral features of the Su-Schrieffer-Heeger (SSH) model. Remarkably, our model shares the SSH models bulk energy spectrum, eigenstates, and Zak phase, hallmarks of its topological character, while introducing a tunable length-scale a quantifying non-locality. This parameter allows for a controlled interpolation between non-local and local regimes. Furthermore, for a specific value of a the exact spectral equivalence to the discrete SSH model is established. Distinct from previous continuous analogues based on Schr\"odinger or Dirac-type Hamiltonians, our approach maintains chiral symmetry, does not require an external potential and features periodic energy bands. On finite domains, the model supports a flat band with zero energy formed by a countable infinite set of exponentially localized zero-energy edge states of topological origin. Beyond SSH, our method lays the foundation for constructing non-local, continuous analogues of a wide class of bipartite and multipartite lattices, opening new paths for theoretical exploration and new challenges for experimental realization in topological quantum matter.

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