Algebraic properties of the Fermi variety for periodic graph operators
Algebraic properties of the Fermi variety for periodic graph operators
复制标题
周期图算子费米簇的代数性质
DOI：
10.1016/j.jfa.2023.110286
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发表时间：
2024
影响因子：
1.7
通讯作者：
Matos, Rodrigo
中科院分区：
文献类型：
--
作者：
Fillman, Jake;Liu, Wencai;Matos, Rodrigo
我们提出了一种方法来估计图上的周期薛定谔算子的费米簇的不可约分量的数量在适当的渐近。我们的主要定理是一个抽象的界限的数量不可约的组成部分劳伦多项式的渐近性。然后，我们将展示如何抽象的界限意味着不可约在许多感兴趣的格，包括在基本细胞，如Lieb格，以及某些模型的过程中获得的图形装饰的一个以上的顶点的例子。
We present a method to estimate the number of irreducible components of the Fermi varieties of periodic Schrödinger operators on graphs in terms of suitable asymptotics. Our main theorem is an abstract bound for the number of irreducible components of Laurent polynomials in terms of such asymptotics. We then show how the abstract bound implies irreducibility in many lattices of interest, including examples with more than one vertex in the fundamental cell such as the Lieb lattice as well as certain models obtained by the process of graph decoration.