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arXiv · 2509.24025

From Quasiperiodicity to a Complete Coloring of the Kohmoto Butterfly

Ram Band·Siegfried Beckus
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Abstract

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.

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Ram Band, Siegfried Beckus. 2025-09-28. From Quasiperiodicity to a Complete Coloring of the Kohmoto Butterfly. https://arxiv.org/abs/2509.24025

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