2017/06/30 by Pieter W. Claeys, Dimitri Van Neck, Stijn De Baerdemacker · 4 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cauchy distribution #Combinatorics #Domain (mathematical analysis) #Eigenvalues and eigenvectors #Geometry #Integrable system #Mathematical analysis #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Partition (number theory) #Physics #Pure mathematics #Quadratic equation #Quantum mechanics #Representation (politics) #cond-mat.stat-mech #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.21468/scipostphys.3.4.028
published as SciPost Phys. 3, 028 (2017) · 21+16 pages, minor revisions compared to the previous version
arxiv created 2017/09/12 · openalex publication_date 2017/10/24 · arxiv updated 2017/10/26 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula. Furthermore, this framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.