Scientific article
Open access

The Eight-Vertex Model and Lattice Supersymmetry

Published inJournal of Statistical Physics, vol. 146, no. 6, p. 1122-1155
  • Open Access - Licence nationale Springer 
Publication date2012

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 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.

Citation (ISO format)
HAGENDORF, Christian, FENDLEY, Paul. The Eight-Vertex Model and Lattice Supersymmetry. In: Journal of Statistical Physics, 2012, vol. 146, n° 6, p. 1122–1155. doi: 10.1007/s10955-012-0430-0
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Article (Published version)
ISSN of the journal0022-4715

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