论文标题
在广义装饰图上的AKLT模型的非呈频谱差距
A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs
论文作者
论文摘要
我们考虑了在装饰版本的简单，连接图的装饰版本上定义的AKLT模型的光谱差距问题。这类装饰的图形是通过用$ n $站点的链条替换所有$ g $的所有边缘来定义的，尤其包括任何装饰的多维晶格。使用Abdul-Rahman等人的工作中使用张量网络状态（TNS）方法。 al。 2020年，我们证明，如果装饰参数大于最大顶点程度的线性函数，则装饰的模型在基态能量上方具有非变化的频谱间隙。
We consider the spectral gap question for AKLT models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of $G$ with a chain of $n$ sites, in particular includes any decorated multi-dimensional lattice. Using the Tensor Network States (TNS) approach from a work by Abdul-Rahman et. al. 2020, we prove that if the decoration parameter is larger than a linear function of the maximal vertex degree, then the decorated model has a nonvanishing spectral gap above the ground state energy.
