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

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 $\mathrm{Schr}\ddot{\mathrm{o}}\mathrm{dinger}$ 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 $\mathrm{Schr}\ddot{\mathrm{o}}\mathrm{dinger}$ 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.

38 pages

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Cited by in corpus (3)

• Second cluster integral from the spectrum of an infinite XXZ spin chain
• Weak ergodicity breaking with isolated integrable sectors
• On the ground state energy scaling in quasi-rung-dimerized spin ladders