Derivations for the MPS overlap formulas of rational spin chains
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908507137114112 |
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| author | Gombor, Tamas |
| author_facet | Gombor, Tamas |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_20234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivations for the MPS overlap formulas of rational spin chains Gombor, Tamas High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems 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. |
| title | Derivations for the MPS overlap formulas of rational spin chains |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2505.20234 |