-Continuum limit of bipartite lattices -- The SSH model
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918192873472000 |
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| author | Diakonos, Fotios K. Schmelcher, P. |
| author_facet | Diakonos, Fotios K. Schmelcher, P. |
| contents | 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 Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | -Continuum limit of bipartite lattices -- The SSH model Diakonos, Fotios K. Schmelcher, P. Quantum Physics Mesoscale and Nanoscale Physics 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 Schrödinger 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. |
| title | -Continuum limit of bipartite lattices -- The SSH model |
| topic | Quantum Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2509.11900 |