Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-05-21
Nucl.Phys. B618 (2001) 689-698
Physics
High Energy Physics
High Energy Physics - Theory
12pages, LaTeX2e, packages used: pstricks, pst-node, pstcol, if these are not available, an eps file will be sent upon request
Scientific paper
10.1016/S0550-3213(01)00491-6
The universal formulation of spin exchange models related to Calogero-Moser models implies the existence of integrable hierarchies, which have not been explored. We show the general structures and features of the spin exchange model hierarchies by taking as examples the well-known Heisenberg spin chain with the nearest neighbour interactions. The energy spectra of the second member of the hierarchy belonging to the models based on the $A_r$ root systems $(r=3,4,5)$ are explicitly and {\em exactly} evaluated. They show many many interesting features and in particular, much higher degree of degeneracy than the original Heisenberg model, as expected from the integrability.
Inozemtsev Vladimir I.
Sasaki Rei
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