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

TL;DR

This paper investigates the eigenvectors and scalar products of a long-range integrable spin chain, focusing on finite size effects and defect contributions, with implications for the N=4 gauge theory's dilatation operator.

Contribution

It determines the defect term at first order in deformation, elucidating its impact on Bethe ansatz equations for the long-range spin chain.

Findings

Identified the defect term at first order in perturbation.

Analyzed how the defect modifies Bethe ansatz equations.

Connected the spin chain model to N=4 gauge theory.

Abstract

In this note, we study the eigenvectors and the scalar products the integrable long-range deformation of a XXX spin chain which 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.