Superlax pairs and infinite symmetries in the 1/r**2 system
Dec, 199210 pages
Published in:
- Phys.Rev.Lett. 70 (1993) 4029-4033
e-Print:
- cond-mat/9212029 [cond-mat]
Report number:
- PRINT-93-0015
View in:
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Abstract: (arXiv)
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the family of interactions. The algebra consists of the commutation between a ``Super- Hamiltonian'', and two other operators, in a Hilbert space that is an enlargement of the original one by introducing fermions. The commutation relations reduce to quantal Ordered Lax equations when projected to the original subspace, and to a statement about the ``Harmonic Lattice Potential'' structure of the Lax operator. These in turn lead to a highly automatic proof of the integrability of these models. In the case of the discrete model, the `` Super-Hamiltonian'' is again an model with a related , providing an interesting hierarchy of models.References(27)
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