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Spin Chains with Dynamical Lattice Supersymmetry

Published inJournal of Statistical Physics, vol. 150, no. 4, p. 609-657
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  • Open Access - Licence nationale Springer 
Publication date2013
Abstract

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.

Citation (ISO format)
HAGENDORF, Christian. Spin Chains with Dynamical Lattice Supersymmetry. In: Journal of Statistical Physics, 2013, vol. 150, n° 4, p. 609–657. doi: 10.1007/s10955-013-0709-9
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ISSN of the journal0022-4715
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