Derivations for the MPS overlap formulas of rational spin chains

Gombor, Tamás (2025) Derivations for the MPS overlap formulas of rational spin chains. JOURNAL OF HIGH ENERGY PHYSICS. ISSN 1126-6708 (In Press)

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Abstract

We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in gl_N symmetric spin chains. This formula expresses the normalized overlap as a product of a MPS-independent Gaudin-determinant ratio and a MPS-dependent scalar factor constructed from eigenvalues of commuting operators, defined via the K-matrix associated with the MPS. Our proof is fully representation- independent and relies solely on algebraic Bethe Ansatz techniques and the KT -relation. We also propose a generalization of the overlap formula to so_N and sp_N spin chains, supported by algebra embeddings and low-rank isomorphisms. These results significantly broaden the class of integrable initial states for which exact overlap formulas are available, with implications for quantum quenches and defect CFTs.

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