2026/08/04 by Kazuki Ikeda, Yaron Oz
Physics and Astronomy · Mathematics · #quant-ph #cond-mat.mes-hall #hep-th #math-ph #math.MP
17 pages, 8 figures
arxiv created 2026/08/04 · arxiv updated 2026/08/05
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 S4. Product frames generate winding numbers in q\mathbb Z+p\mathbb Z, so global factorization is possible exactly when C2 is divisible by gcd(p,q); in particular, odd C2 obstructs a 2×2 factorization. We illustrate the two settings with finite eight-level Hamiltonians and give pumping and occupied-projector tomography protocols for their readout.