Eigenvectors and scalar products for long range interacting spin chains II: the finite size effects

Abstract : In this note, we study the eigenvectors and the scalar products the integrable long-range deformation of the XXX spin chain defined in [1]. The model is solved exactly by algebraic Bethe ansatz, and it coincides in the bulk with the Inozemtsev spin chain. At the closing point it contains a defect which effectively removes the wrapping interactions. Here we concentrate on determining the defect term for the first non-trivial order in perturbation in the deformation parameter and how it affects the Bethe ansatz equations. Our study is motivated by the relation with the dilatation operator of the N = 4 gauge theory in the su(2) sector. Introduction: Long range spin chains. In this paper we consider long-range integrable deformations of the XXX spin-1/2 spin chain. There are several methods to turn a nearest-neighbor spin chain into a long-range ones. One method, used in [2, 3], is to deform the conserved charges according to d dλ Q r (λ) = i [χ(λ), Q r (λ)] , (1)
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Didina Serban. Eigenvectors and scalar products for long range interacting spin chains II: the finite size effects. Journal of High Energy Physics, Springer Verlag (Germany), 2013, 1308 (8), pp.128. ⟨10.1007/JHEP08(2013)128⟩. ⟨cea-01227856⟩

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