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Baker--Akhiezer sections from Higgs bundles and Landau levels in hyperbolic band theory
As observed by Kienzle and the second author, rank-two $\mathcal{O}(3)$-twisted Higgs bundles on the projective line encode all hyperbolic crystals of genus two: the spectral curves are the unit cells, and the Hitchin fibers are the abelian Brillouin zones. In a uniform magnetic field of two flux qu
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