Rare Flat Bands for Periodic Graph Operators
Spectral Theory
2025-03-27 v2 Mathematical Physics
Commutative Algebra
Algebraic Geometry
Combinatorics
math.MP
Abstract
As a corollary of our main results, we prove that for any connected -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.
Cite
@article{arxiv.2503.03632,
title = {Rare Flat Bands for Periodic Graph Operators},
author = {Matthew Faust and Wencai Liu},
journal= {arXiv preprint arXiv:2503.03632},
year = {2025}
}
Comments
28 pages, 1 figure