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arXiv · 2503.03632

Rare Flat Bands for Periodic Graph Operators

Matthew Faust·Wencai Liu
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Abstract

As a corollary of our main results, we prove that for any connected $\mathbb{Z}^d$-periodic graph, when edge weights and potentials are treated as variables, the corresponding periodic graph operators generically (i.e., outside a proper algebraic subset of the variable space) do not have flat bands.

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Matthew Faust, Wencai Liu. 2025-03-25. Rare Flat Bands for Periodic Graph Operators. https://arxiv.org/abs/2503.03632

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