发表机构
Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文定义纯态对的Z₂指标，将其应用于一维超导体的多体马约拉纳数，证明该指标可分类自同构路径分支，为相互作用一维超导体的拓扑分类提供新方法。
AI 中文摘要
我们对幺正C*-代数上局部可比的宇称不变纯态定义了相对Z₂指标𝒩(ω₁,ω₂)，证明该指标良定、具乘法性、在保宇称自同构下不变且在范数拓扑中局部常值。对一维自对偶CAR代数，我们将该构造应用于半链自同构σ，对σ-局部宇称不变纯态定义多体马约拉纳数𝒩_σ(ω):=𝒩(ω,ω∘σ)，在准自由希尔伯特-施密特 regime 中该指标与常规单体马约拉纳数一致。随后我们引入对称局部自同构路径，证明𝒩_σ可完全分类所得自同构路径分支，该路径等价性保留体马约拉纳数，但可能丢失相对零维宇称障碍。
英文摘要
We define a relative $\mathbb{Z}_2$-index $\mathcal{N}(ω_1,ω_2)$ for locally-comparable, parity-invariant pure states on a unital $C^*$-algebra. We prove that the index is well-defined, multiplicative, invariant under parity-preserving automorphisms, and locally constant in the norm topology. For the one-dimensional self-dual CAR algebra, we apply this construction to the half-chain automorphism $σ$ and define the many-body Majorana number $\mathcal{N}σ(ω):=\mathcal{N}(ω,ω\circσ)$ for parity-invariant $σ$-local pure states. In the quasi-free Hilbert--Schmidt regime, this index agrees with the usual single-body Majorana number. We then introduce symmetric local automorphism paths and prove that $\mathcal{N}_σ$ completely classifies the resulting automorphic-path-components. This automorphic-path equivalence retains the bulk Majorana number but may forget a relative zero-dimensional parity obstruction.
