From Quasiperiodicity to a Complete Coloring of the Kohmoto Butterfly
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| Format: | Preprint |
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2025
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| _version_ | 1866908567970250752 |
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| author | Band, Ram Beckus, Siegfried |
| author_facet | Band, Ram Beckus, Siegfried |
| contents | The spectra of the Kohmoto model give rise to a fractal phase diagram, known as the Kohmoto butterfly. The butterfly encapsulates the spectra of all periodic Kohmoto Hamiltonians, whose index invariants are sought after. Topological methods - such as Chern numbers - are ill defined due to the discontinuous potential, and hence fail to provide index invariants. This Letter overcomes that obstacle and provides a complete classification of the Kohmoto model indices. Our approach encodes the Kohmoto butterfly as a spectral tree graph, reflecting the quasiperiodic nature via the periodic spectra. This yields a complete coloring of the phase diagram and a new perspective on other spectral butterflies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_24025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Quasiperiodicity to a Complete Coloring of the Kohmoto Butterfly Band, Ram Beckus, Siegfried Mathematical Physics Quantum Physics The spectra of the Kohmoto model give rise to a fractal phase diagram, known as the Kohmoto butterfly. The butterfly encapsulates the spectra of all periodic Kohmoto Hamiltonians, whose index invariants are sought after. Topological methods - such as Chern numbers - are ill defined due to the discontinuous potential, and hence fail to provide index invariants. This Letter overcomes that obstacle and provides a complete classification of the Kohmoto model indices. Our approach encodes the Kohmoto butterfly as a spectral tree graph, reflecting the quasiperiodic nature via the periodic spectra. This yields a complete coloring of the phase diagram and a new perspective on other spectral butterflies. |
| title | From Quasiperiodicity to a Complete Coloring of the Kohmoto Butterfly |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2509.24025 |