多体几何相中的连通性阶定律与条件极小机制识别
A Connectivity-Order Law and Conditional Minimal-Mechanism Identification in Many-Body Geometric Phases
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中文总结 AI 辅助
该研究针对多体几何相，提出连通性阶定律，结合Wilson计算与Ramay检测，实现了条件极小机制识别，可区分多体相互作用的直接与间接路径并定位有限分辨率边界。
中文摘要 AI 辅助
单工作点下的多qubit几何相的值无法揭示其是直接产生还是通过一系列连通的低体相互作用产生的。对于解析、带隙、非简并阿贝尔和乐，我们联合解析逻辑支撑与独立校准的耦合支撑。每个非零连通响应必须涉及一个连通并覆盖目标的激活集，且必须包含每个激活耦合的一个因子，由此得到尖锐的起始界ν_S ≥ τ_E(S)。同一选择定律局部适用于投影Berry曲率。相反，无限制的有限维构造可同时实现连通覆盖条件允许的所有响应，使该条件在本定理类内是必要且充分的。操作上，同时置信带可在控制假阳性的同时验证检测到的混合响应；因子为2的分离条件还可恢复精确的库相对响应极小值。在完整字典中，每个极小覆盖响应的非平凡性通常是必要且充分的，以使得这些极小值与极小校准机制一致。三qubit Wilson计算区分了具有相同端点相位的直接和对介导路径，合成Ramay检测定位了有限分辨率边界。
英文摘要
The value of a multiqubit geometric phase at a single operating point does not reveal whether it was generated directly or through a connected sequence of lower-body interactions. For analytic, gapped, nondegenerate Abelian holonomies, we jointly resolve logical support and independently calibrated coupling support. Every nonzero connected response must involve an active set that connects and covers the target and must contain one factor of each active coupling, yielding the sharp onset bound $ν_S \geq τ_E(S)$. The same selection law applies locally to projected Berry curvature. Conversely, an unrestricted finite-dimensional construction realizes all responses allowed by the connected-cover condition simultaneously, making the condition necessary and sufficient within this theorem class. Operationally, simultaneous confidence bands certify detected mixed responses while controlling false positives; a factor-of-two separation condition additionally recovers exact library-relative response minima. In a complete dictionary, nontriviality of every minimal-cover response is generically necessary and sufficient for these minima to coincide with the minimal calibrated mechanisms. Three-qubit Wilson calculations distinguish direct and pair-mediated routes with the same endpoint phase, and a synthetic Ramsey audit locates the finite-resolution boundary.
