A family of spin-S chain representations of SU(2) level k Wess-Zumino-Witten models

ORAL

Abstract

We investigate a family of spin-$S$ chain Hamiltonians recently introduced by one of us [M. Greiter, Mapping of Parent Hamiltonians, Springer Tracts in Modern Phyiscs, Vol 244 (Springer, Berlin, 2011)]. For $S=1/2$, it corresponds to the Haldane--Shastry model. For general spin $S$, we numerically show that the low--energy theory of these spin chains is described by the SU(2)$_{k}$ Wess--Zumino--Witten model with coupling $k=2S$. In particular, we investigate the $S=1$ model whose ground state is given by a Pfaffian for even number of sites $N$. We reconcile aspects of the spectrum of the Hamiltonian for arbitrary $N$ with trial states obtained by Schwinger projection of two Haldane--Shastry chains.

–

Authors

  • Martin Greiter

    Institut fuer Festkoerperphysik, KIT, Postfach 3640, 76021 Karlsruhe, Germany

  • Ronny Thomale

    Department of Physics, Stanford University, Stanford University, Department of Physics, Stanford University, Stanford, CA 94305, USA

  • Stephan Rachel

    Yale University, Department of Physics, Yale University, New Haven, CT 06520, USA, Department of Physics, Yale University, 217 Prospect Street, New Haven, CT 06520, USA

  • Peter Schmitteckert

    Institute fuer Nanotechnologie, KIT, 76344 Eggenstein-Leopoldshafen, Germany