论文标题
在一个维
Elementary derivation of the stacking rules of invertible fermionic topological phases in one dimension
论文作者
论文摘要
在任何封闭的空间歧管上，可逆的费米拓扑（IFT）阶段是物质与非等级基态的隔离阶段。当施加开放的边界条件时，非平凡的IFT阶段支持无间隙的边界自由度。具有内部对称组$ g^{\，} _ {f} $的一维空间中的独特IFT阶段的特征是索引$（[（ν，ρ）]，[μ]）$的三重态。我们的主要结果是对任何给定的内部对称组的一维IFT阶段的费米子堆叠规则的基本推导，$ g^{\，} _ {f} $从边界的角度来看$） $（[（（ν^{\，} _ {1}，ρ^{\，} _ {1}）]，[μ^{\，} _ {1}]）$和$（[（ν^{\，} _ {2}，ρ^{\，} _ {2}）]，[μ^{\，} _ {2}]）$。
Invertible fermionic topological (IFT) phases are gapped phases of matter with nondegenerate ground states on any closed spatial manifold. When open boundary conditions are imposed, nontrivial IFT phases support gapless boundary degrees of freedom. Distinct IFT phases in one-dimensional space with an internal symmetry group $G^{\,}_{f}$ have been characterized by a triplet of indices $([(ν,ρ)],[μ])$. Our main result is an elementary derivation of the fermionic stacking rules of one-dimensional IFT phases for any given internal symmetry group $G^{\,}_{f}$ from the perspective of the boundary, i.e., we give an explicit operational definition for the boundary representation $([(ν^{\,}_{\wedge},ρ^{\,}_{\wedge})],[μ^{\,}_{\wedge}])$ obtained from stacking two IFT phases characterized by the triplets of boundary indices $([(ν^{\,}_{1},ρ^{\,}_{1})],[μ^{\,}_{1}])$ and $([(ν^{\,}_{2},ρ^{\,}_{2})],[μ^{\,}_{2}])$, respectively.
