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Lattice fermion models with supersymmetry

Paul Fendley·Bernard Nienhuis·Kareljan Schoutens
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Abstract

We investigate a family of lattice models with manifest N=2 supersymmetry. The models describe fermions on a 1D lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special properties arising from the supersymmetry, and present Bethe ansatz solutions of the simplest models. We display the connections of the k=1 model with the spin-1/2 antiferromagnetic XXZ chain at Δ=-1/2, and the k=2 model with both the su(2|1)-symmetric tJ model in the ferromagnetic regime and the integrable spin-1 XXZ chain at Δ=-1/\sqrt{2}. We argue that these models include critical points described by the superconformal minimal models.

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Paul Fendley, Bernard Nienhuis, Kareljan Schoutens. 2003-09-21. Lattice fermion models with supersymmetry. https://doi.org/10.1088/0305-4470%2F36%2F50%2F004

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