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Spin Chains with Dynamical Lattice Supersymmetry

Hagendorf, Christian

In: Journal of Statistical Physics, 2013, vol. 150, no. 4, p. 609-657

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    Titre
    • Spin Chains with Dynamical Lattice Supersymmetry
    Auteur
    • Hagendorf, Christian. Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, CP 64, 1211, Geneva 4, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Statistical Physics, 2013, vol. 150, no. 4, p. 609-657. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:321694
    Summary
    Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on periodic lattices is formulated. Any of its solutions leads to a supersymmetric spin chain. It is shown that a class of special solutions at arbitrary spin gives the lattice equivalents of the $\mathcal{N}=(2,2)$ superconformal minimal models. The case of spin one is investigated in detail: in particular, it is shown that the Fateev-Zamolodchikov chain and its off-critical extension possess a lattice supersymmetry for all its coupling constants. Its supersymmetry singlets are thoroughly analysed, and a relation between their components and the weighted enumeration of alternating sign matrices is conjectured