Spin chains from super-models

Details Spin chains from super-models Spin chains from super-models

2000-12-07

arxiv.org/abs/hep-th/0012058v3

J.Phys.Soc.Jap. 70 (2001) 3225-3237

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, RevTeX, No figures, v1; Corrected typos, Added minor clarifications, v2; Added discussions, version to appear in JPS

Scientific paper

10.1143/JPSJ.70.3225

We construct and study a class of N particle supersymmetric Hamiltonians with nearest and next-nearest neighbor inverse-square interaction in one dimension. We show that inhomogeneous XY models in an external non-uniform magnetic field can be obtained from these super-Hamiltonians in a particular limit decoupling the fermionic degrees of freedom from the kinematic ones. We further consider a suitable deformation of these super-models such that inhomogeneous XXZ Hamiltonians in an external non-uniform magnetic field are obtained in the same limit. We show that this deformed Hamiltonian with rational potential is, (i) mapped to a set of free super-oscillators through a similarity transformation and (ii) supersymmetric in terms of a new, non-standard realization of the supercharge. We construct many exact eigenstates of this Hamiltonian and discuss about the applicability of this technique to other models.

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