Derivations for the MPS overlap formulas of rational spin chains

Abstract

We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in ${\mathfrak{gl}}_N$ 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 ${\mathfrak{so}}_N$ and ${\mathfrak{sp}}_N$ 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.

arXiv commenttypos corrected

Cited by in corpus (1)

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