Pieter W. Claeys, Dimitri Van Neck, Stijn De Baerdemacker
SciPost Phys. 3, 028 (2017) ·
published 24 October 2017

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We present the inner products of eigenstates in integrable RichardsonGaudin models from two different perspectives and derive two classes of Gaudinlike determinant expressions for such inner products. The requirement that one of the states is onshell 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. 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.