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Lattice Models with N=2 Supersymmetry

Paul Fendley·Kareljan Schoutens·Jan de Boer
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Abstract

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q^+ and Q^- yield the Hamiltonian H={Q^+,Q^-} on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers. The Hamiltonian of our simplest model contains a hopping term and a repulsive potential, as well as the hard-core repulsion. We discuss these models from a variety of perspectives: using a fundamental relation with conformal field theory, via the Bethe ansatz, and using cohomology methods. The simplest model provides a manifestly-supersymmetric lattice regulator for the supersymmetric point of the massless 1+1-dimensional Thirring (Luttinger) model. We discuss the ground-state structure of this same model on more complicated graphs, including a 2-leg ladder, and discuss some generalizations.

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Paul Fendley, Kareljan Schoutens, Jan de Boer. 2002-10-17. Lattice Models with N=2 Supersymmetry. https://doi.org/10.1103/physrevlett.90.120402

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