Generalized Haldane-Shastry Models as Supersymmetric Partners of the Calogero-Sutherland Type Models

Details Generalized Haldane-Shastry Models as Supersymmetric Partners of the Calogero-Sutherland Type Models Generalized Haldane-Shastry Models as Supersymmetric Partners of the Calogero-Sutherland Type Models

1997-02-02

arxiv.org/abs/cond-mat/9702012v2

Physics

Condensed Matter

Statistical Mechanics

Paper withdrawn

Scientific paper

We consider the supersymmetric Calogero-Sutherland type N-particle problems in one dimension and show that the corresponding fermionic part can be identified with the generalized X-Y models in the presence of an inhomogeneous magnetic field. In particular we show that the generalized Haldane-Shastry models (with magnetic field) are themselves the fermionic partners of the Calogero-Sutherland type models. Several such models are discussed and a recipe is given for constructing spin models and finding their ground state energy from the corresponding N-particle problems.

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