具有循环群作用的周期量子图Fermi面可约性

Reducibility of the Fermi Surface forPeriodic Quantum Graphs with Cyclic Group Actions

摘要: 本文通过将给定的单层周期量子图与具有循环群作用的正三边形做笛卡尔积构造了一类“三层”量子图，其中正三边形被称为连接图，得到“三层”量子图的函数空间分解和算子分解，证明了其Fermi面可约，并将结论推广到连接图为具有循环群作用的正n边形情况。

Abstract: This paper constructs a class of"three-layer" quantum graphs by taking the Cartesian product of a given single-layer periodic quantum graph with an equilateral triangle (referred to as the connecting graph) endowed with a cyclic group action. The function space decomposition and operator decomposition of the resulting"three-layer" quantum graphs are derived. It is proven that their Fermi surfaces are reducible. Furthermore, the conclusions are generalized to the case where the connecting graph is a regular n-gon with a cyclic group action.