Violations of the String Hypothesis in the Solutions of the Bethe Ansatz Equations in the XXX-Heisenberg

Details Violations of the String Hypothesis in the Solutions of the Bethe Ansatz Equations in the XXX-Heisenberg Violations of the String Hypothesis in the Solutions of the Bethe Ansatz Equations in the XXX-Heisenberg

1993-04-19

arxiv.org/abs/hep-th/9304078v2

Phys.Lett. B319 (1993) 209-214

Physics

High Energy Physics

High Energy Physics - Theory

18 pages. revised to amplify credit, in plain tex with macropackage psbox (available from the net)

Scientific paper

10.1016/0370-2693(93)90804-Q

We study the equations for the quasi-momenta which characterize the wave-functions in the Bethe ansatz for the XXX-Heisenberg model. We show in a simple analytical fashion, that the usual ``string hypothesis" incorrectly predicts the number of real solutions and the number of complex solutions for $N>21$ in the sector with two spins flipped, confirming the work of Essler et al. Two complex pair solutions drop out and form two additional real pair solutions. We also introduce a new set of variables which allows the equations to be written as a single polynomial equation in one variable. We consider in some detail the case of three spins flipped.

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