Spin chains with dynamical lattice supersymmetry
Christian Hagendorf, Université de Genève
Starting from simple observations about the spectrum of the spin-1/2 XXZ and XYZ Heisenberg chains at particular anisotropy I will show how to construct a representation of the N=(2,2) supersymmetry algebra on the lattice. The supercharges are dynamical: they change the number of sites. The construction generalises to higher spin. In particular, it allows to identify lattice precursors of the N=(2,2) superconformal minimal models. The supersymmetry allows to prove the existence of zero-energy ground states which have often rich properties related to enumerative combinatorics. I will discuss in detail the case of the Fateev-Zamolodchikov chain at spin one whose ground-state components are related to the weighted enumeration of alternating sign matrices.