The eight-vertex model and lattice supersymmetry

TL;DR

This paper reveals a hidden N=(2,2) supersymmetry in the XYZ spin chain along a special coupling line, extending to the eight-vertex model, with implications for ground state conjectures and spectrum correspondence.

Contribution

It introduces a non-local lattice supersymmetry in the XYZ chain and derives supercharges from Bethe ansatz, connecting it to supersymmetric fermion chains.

Findings

Identification of hidden supersymmetry in XYZ chain

Derivation of supercharges from Bethe ansatz

Conjectures on ground states for odd-length chains

Abstract

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.