We show that the XYZ spin chain along the special line of couplings J x J y +J x J z +J y J z =0 possesses a hidden $\\mathcal{N}=(2,2)$ 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 chainWe show that the XYZ spin chain along the special line of couplings J x J y +J x J z +J y J z =0 possesses a hidden $\\mathcal{N}=(2,2)$ 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

Jan 1, 201217 citations

Analytic theory of the eight-vertex model

Vladimir V. Bazhanov, Vladimir V. Mangazeev

arXiv:hep-th/0609153Nuclear Physics BJan 14, 200734 citations

We show that the XYZ spin chain along the special line of couplings J x J y +J x J z +J y J z =0 possesses a hidden

\\mathcal{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