Year: 2025
Type: article
Abstract: A bstract We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in $$ {\mathfrak{gl}}_N $$ 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 $$ {\mathfrak{so}}_N $$ so N and $$ {\mathfrak{sp}}_N $$ 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.
Source: Journal of High Energy Physics
Author: Tamas Gombor
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414807710