A note on the eigenvectors of long-range spin chains and their scalar products

Details A note on the eigenvectors of long-range spin chains and their scalar products A note on the eigenvectors of long-range spin chains and their scalar products

2012-03-26

arxiv.org/abs/1203.5842v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

In this note, we propose an expression for the eigenvectors and scalar products for a class of spin chains with long-range interaction and su(2) symmetry. This class includes the Inozemtsev spin chain as well as the BDS spin chain, which is a reduction of the one-dimensional Hubbard model at half-filling to the spin sector. The proposal is valid for large spin chains and is based on the construction of the monodromy matrix using the Dunkl operators. For the Inozemtsev model these operators are known explicitly. This construction gives in particular the eigenvectors of the dilatation operator of the N=4 gauge theory in the su(2) sector up to three-loop order, as well as their scalar products. We suggest how this will affect the expression for the three-point functions obtained by I. Kostov and how to include the all-loop interaction.

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