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arXiv · 0902.1335

Three-magnon problem for exactly rung-dimerized spin ladders: from general outlook to Bethe Ansatze

P. N. Bibikov
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Abstract

Three-magnon problem for exactly rung-dimerized spin ladder is brought up separately at all total spin sectors. At first a special duality transformation of the $\rm Schr\ddot odinger$ equation is found within general outlook. Then the problem is treated within Coordinate Bethe Ansatze. A straightforward approach is developed to obtain pure scattering states. At values S=0 and S=3 of total spin the $\rm Schr\ddot odinger$ equation has the form inherent in the $XXZ$ chain. For $S=1,2$ solvability holds only in five previously found {\it completely integrable} cases. Nevertheless a partial S=1 Bethe solution always exists even for general non integrable model. Pure scattering states for all total spin sectors are presented explicitly.

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P. N. Bibikov. 2009-02-08. Three-magnon problem for exactly rung-dimerized spin ladders: from general outlook to Bethe Ansatze. https://doi.org/10.1088/1751-8113%2F42%2F31%2F315212

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