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The Eight-Vertex Model and Lattice Supersymmetry

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Abstract

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.

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Authors and Affiliations

  1. Section des Mathématiques, Université de Genève, 2–4 rue du Lièvre, CP 64, 1211, Genève 4, Switzerland

    Christian Hagendorf

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, USA

    Christian Hagendorf

  3. Department of Physics, University of Virginia, 382 McCormick Rd, Charlottesville, VA, 22904, USA

    Paul Fendley

  4. Microsoft Station Q, University of California, Santa Barbara, CA, 93106, USA

    Paul Fendley

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  1. Christian Hagendorf
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  2. Paul Fendley
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Correspondence to Christian Hagendorf.

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Hagendorf, C., Fendley, P. The Eight-Vertex Model and Lattice Supersymmetry. J Stat Phys 146, 1122–1155 (2012). https://doi.org/10.1007/s10955-012-0430-0

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