通过Bargmann不变量实现Weyl手性与Kitaev拓扑
Weyl Chirality and Kitaev Topology through Bargmann Invariants
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中文总结 AI 辅助
本文利用Bargmann不变量构造有限态几何，探测Weyl系统的手性及Kitaev链的拓扑相，提供基于量子态重叠的替代方法。
中文摘要 AI 辅助
我们将基于Bargmann不变量的有限态几何表述应用于两带Weyl哈密顿量和p波超导体的一维Kitaev模型。对于Weyl系统，一个对称-反对称化的三阶Bargmann组合选择局域赝自旋几何中对手性敏感的分量，并扩展到两带晶格Weyl模型。对于Kitaev链，一个涉及三阶Bargmann不变量和二阶重叠因子的归一化比率消除了对中间态的依赖，并重现了其两个能隙相之间的$Z_2$区分。我们进一步构建了一个连接局域Majorana边缘模轮廓与有限能量BdG态的四阶回路，以及一个涉及相反Weyl赝自旋扇区的交替四阶回路。这些构造说明了合适的Bargmann组合如何通过量子态重叠直接探测手性敏感、拓扑和高阶几何信息，提供了一种无需底层态空间几何连续描述的基于态的可选途径。
英文摘要
We apply a finite-state geometric formulation based on Bargmann invariants to a two-band Weyl Hamiltonian and the one-dimensional Kitaev model of a p-wave superconductor. For the Weyl system, a symmetry-antisymmetrized third-order Bargmann combination selects the chirality-sensitive component of the local pseudospin geometry and extends to a two-band lattice Weyl model. For the Kitaev chain, a normalized ratio involving a third-order Bargmann invariant and a second-order overlap factor removes the dependence on an intermediate state and reproduces the $Z_2$ distinction between its two gapped phases. We further construct a fourth-order loop connecting localized Majorana edge-mode profiles with finite-energy BdG states and an alternating fourth-order loop involving opposite Weyl pseudospin sectors. These constructions illustrate how suitable Bargmann combinations can probe chirality-sensitive, topological, and higher-order geometric information directly through quantum-state overlaps, providing an alternative state-based route without requiring a continuous description of the underlying state-space geometry.
