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Irreducibility of the Bloch Variety for Finite-Range Schr\"odinger Operators

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arxiv 2107.06447 v2 pith:ZJ6Y7ANX submitted 2021-07-14 math-ph math.MPmath.SP

Jake Fillman , Wencai Liu , Rodrigo Matos This is my paper · ORCID
classification math-phmath.MPmath.SP
keywords blochlatticevarietyfinite-rangeodingeroperatorsschrarbitrary
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We study the Bloch variety of discrete Schr\"odinger operators associated with a complex periodic potential and a general finite-range interaction, showing that the Bloch variety is irreducible for a wide class of lattice geometries in arbitrary dimension. Examples include the triangular lattice and the extended Harper lattice.

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