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Rare Flat Bands for Periodic Graph Operators

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arxiv 2503.03632 v2 pith:GUST2O4T submitted 2025-03-05 math.SP math-phmath.ACmath.AGmath.COmath.MP

Matthew Faust , Wencai Liu This is my paper · ORCID
classification math.SPmath-phmath.ACmath.AGmath.COmath.MP
keywords graphperiodicbandsflatoperatorsalgebraicconnectedcorollary
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Absence of flat bands for discrete periodic graph operators with generic potentials

    math.SP 2025-09 conditional novelty 8.0 of 10

    Generic potentials on any connected periodic graph produce no flat bands.

  2. Two Instances of Chaos in Deterministic and Quantum Dynamical Systems

    math.DS 2026-07 conditional novelty 7.0 of 10

    Ergodic torus automorphisms with 2D center are stably ergodic, and graph families with regular integrated density of states have asymptotically dense delocalization.

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