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arXiv · 2607.01137

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

Yi Liang
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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, with the circumference taken to infinity at fixed prefix and the prefix enlarged only afterward, full-RDM convergence together with the odd-even Toeplitz/Fisher-Hartwig endpoint yields an excess entropy $\tfrac12\log2$ over the homogeneous chain, whereas the matched invertible $\eta$ defect yields zero. The exact character of the same twisted Hamiltonian, jointly resolved by energy and modified translation, records the finite-size roots and their multiplicities, retains chirality in the marked scaling limit, and, using the standard Ising character identities, resolves the four Virasoro towers of the Ising duality-twisted sector.

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Yi Liang. 2026-07-01. Physical reduced states and continuum characters of the lattice Kramers-Wannier defect. https://arxiv.org/abs/2607.01137

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