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arXiv · 1408.4403

Bethe ansatz solvability and supersymmetry of the $M_2$ model of single fermions and pairs

Christian Hagendorf·Thessa B. Fokkema·Liza Huijse
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Abstract

A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified. The relation between this manifold and the existence of additional, so-called dynamic, supersymmetries is discussed. The ground states are analysed with the help of cohomology techniques, and their exact finite-size Bethe roots are found. Moreover, through analytical and numerical studies it is argued that the model provides a lattice version of the $\mathcal N=1$ super-sine-Gordon model at a particular coupling where an additional $\mathcal N=(2,2)$ supersymmetry is present. The dynamic supersymmetry is shown to allow an exact determination of the gap scaling function of the model.

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Christian Hagendorf, Thessa B. Fokkema, Liza Huijse. 2014-08-19. Bethe ansatz solvability and supersymmetry of the $M_2$ model of single fermions and pairs. https://doi.org/10.1088/1751-8113/47/48/485201

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