A three-magnon problem for an exactly rung-dimerized spin ladder is brought up separately in all total spin sectors. At first, a special duality transformation of the Schrödinger equation is found within the general outlook. Then the problem is treated within the coordinate Bethe ansatz. A straightforward approach is developed to obtain pure scattering states. At values S = 0 and S = 3 of total spin, the Schrödinger equation has a form inherent in the XXZ chain. At S = 1, 2, solvability holds only in five previously found completely integrable cases. Nevertheless, even in a general non-integrable case, there are some special Bethe solutions in both S = 1 and S = 2 sectors. Pure scattering states in all total spin sectors are presented explicitly.A three-magnon problem for an exactly rung-dimerized spin ladder is brought up separately in all total spin sectors. At first, a special duality transformation of the Schrödinger equation is found within the general outlook. Then the problem is treated within the coordinate Bethe ansatz. A straightforward approach is developed to obtain pure scattering states. At values S = 0 and S = 3 of total spin, the Schrödinger equation has a form inherent in the XXZ chain. At S = 1, 2, solvability holds only in five previously found completely integrable cases. Nevertheless, even in a general non-integrable case, there are some special Bethe solutions in both S = 1 and S = 2 sectors. Pure scattering states in all total spin sectors are presented explicitly.

arXiv:0902.1335Journal of Physics A Mathematical and TheoreticalJul 16, 20097 citations

Three-magnon bound states in exactly rung-dimerized spin ladders

P. N. Bibikov

Three magnon bound states in all total spin sectors of general nonintegrable exactly rung-dimerized spin ladder are obtained by Bethe Ansatz. Basing on this result a dispersion law for $m$ -magnon ( $m>3$ ) bound states is conjectured. It is suggested that (depending on correlations between coupling constants) a behavior of the gas parameter (density of rung-triplets) on the boundary of the rung-dimerized phase may either be smooth or have a leap.Three magnon bound states in all total spin sectors of general nonintegrable exactly rung-dimerized spin ladder are obtained by Bethe Ansatz. Basing on this result a dispersion law for $m$-magnon ($m>3$) bound states is conjectured. It is suggested that (depending on correlations between coupling constants) a behavior of the gas parameter (density of rung-triplets) on the boundary of the rung-dimerized phase may either be smooth or have a leap.

arXiv:1003.3472Mar 17, 20100 citations

Three magnon bound states in all total spin sectors of general nonintegrable exactly rung-dimerized spin ladder are obtained by Bethe Ansatz. Basing on this result a dispersion law for

m

-magnon (

m>3

) bound states is conjectured. It is suggested that (depending on correlations between coupling constants) a behavior of the gas parameter (density of rung-triplets) on the boundary of the rung-dimerized phase may either be smooth or have a leap.