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Direct proof for the Scalar Product with Bethe eigenstate in Spin chains

2000/12/22 by A. A. Ovchinnikov, А. А. Овчинников, Ovchinnikov, A. A.
Materials Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Magnetism in coordination complexes #Mathematical Physics (math-ph) #Quantum many-body systems #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.math-ph/0012042

LaTex, 12 pages

arxiv created 2000/12/22 · openalex publication_date 2000/12/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the simple and direct proof of the determinantal formula for the scalar product of Bethe eigenstate with an arbitrary dual state. We briefly review the direct calculation of the general scalar product with the help of the factorizing operator and the construction of the factorizing operator itself. We also comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state.

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