AI 中文总结
本文研究孤立占据多重态的全局子系统结构阻碍，通过过渡函数比较刻画该阻碍，结合不同因子维数条件分析混合陈类，以八能级哈密顿量为例并给出相关读取协议。
AI 中文摘要
孤立的占据多重态可能存在局域张量积描述，却无全局一致的子系统结构。我们通过比较占据多重态的过渡函数与两个候选子系统中独立基变换生成的过渡函数，来刻画这种阻碍。当指定闭合曲面上的秩1扇区分解时，所得商结构会去除行与列加性陈数数据，得到混合陈类；扇区标签的动量相关混合会引入运动直线的高斯-科达齐曲率，而在标签守恒极限下，混合类由交叉索利斯泵测量。当仅指定因子维数p和q时，比较在S⁴上的秩pq丛的 clutching映射层面进行；乘积框架在qℤ+pℤ中生成绕数，因此仅当C₂可被gcd(p,q)整除时才存在全局分解，特别地，奇数C₂会阻碍2×2分解。我们用有限八能级哈密顿量说明这两种情形，并给出用于读取的泵浦和占据投影层析成像协议。
英文摘要
An isolated occupied multiplet may admit local tensor-product descriptions without a globally consistent subsystem structure. We characterize the obstruction by comparing the transition functions of the occupied multiplet with those generated by independent basis changes in the two candidate subsystems. When a decomposition into rank-one sectors over a closed surface is specified, the resulting quotient removes row- and column-additive Chern data and yields mixed Chern classes. Momentum-dependent mixing of the sector labels adds the Gauss--Codazzi curvature of the moving lines, while in the label-conserving limit the mixed class is measured by a crossed Thouless pump. When only the factor dimensions $p$ and $q$ are specified, the comparison is made at the level of the clutching map of a rank-$pq$ bundle over $S^4$. Product frames generate winding numbers in $q\mathbb Z+p\mathbb Z$, so global factorization is possible exactly when $C_2$ is divisible by $\gcd(p,q)$; in particular, odd $C_2$ obstructs a $2\times2$ factorization. We illustrate the two settings with finite eight-level Hamiltonians and give pumping and occupied-projector tomography protocols for their readout.
Comments17 pages, 8 figures
