The eight-vertex model and lattice supersymmetry

Details The eight-vertex model and lattice supersymmetry The eight-vertex model and lattice supersymmetry

2011-09-19

arxiv.org/abs/1109.4090v1

J. Stat. Phys. 146 (2012), 1122-1155

Physics

Mathematical Physics

40 pages, 6 figures, TikZ

Scientific paper

10.1007/s10955-012-0430-0

We show that the XYZ spin chain along the special line of couplings J_xJ_y+J_xJ_z+J_yJ_z=0 possesses a hidden N=(2,2) supersymmetry. This lattice supersymmetry is non-local and changes the number of sites. It extends to the full transfer matrix of the corresponding eight-vertex model. In particular, it is shown how to derive the supercharges from Baxter's Bethe ansatz. This analysis leads to new conjectures concerning the ground state for chains of odd length. We also discuss a correspondence between the spectrum of this XYZ chain and that of a manifestly supersymmetric staggered fermion chain.

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