Physical reduced states and continuum characters of the lattice Kramers-Wannier defect

Abstract:A non-invertible topological line fixes global defect data but does not select a reduced density matrix in a spatially twisted sector. For the Kramers-Wannier defect of the critical Ising chain, we choose the equal-weight incoherent mixture of the two charge-sector ground states and reduce it to the ordinary full spin algebra of a complete non-wrapping prefix anchored at the defect endpoint. The finite-size RDM is the convex average of two charge-sector RDMs rather than a sign-zero Gaussian proxy, and an exact descended antiunitary enforces many-body Kramers pairing without determining the entropy. In the strict nested limit (circumference to infinity at fixed prefix, followed by enlargement of the prefix), full-RDM convergence together with the odd-even Toeplitz/Fisher-Hartwig endpoint yields an excess entropy $\tfrac12\log 2$ over the homogeneous chain, whereas the matched invertible $\eta$ defect yields zero. The exact joint energy-modified-translation character of the same twisted Hamiltonian records the finite-size roots and their multiplicities, retains chirality in the marked scaling limit, and resolves the four Virasoro towers of the Ising duality-twisted sector.

51 pages, 3 figures. Expanded version with the physical equal-charge spin RDM, the ordered-limit entropy theorem, and the exact finite-size joint energy-modified-translation character. Code: this https URL

arXiv:2607.01137 [quant-ph]

(or arXiv:2607.01137v3 [quant-ph] for this version)