Higher symmetries in the spin-one Zamolodchikov-Fateev hamiltonian with a finite number of sites and toroidal boundary conditions. Spectra and operator content of N = 1 superconformal systems

Abstract

The finite-size scaling spectra of the antiferromagnetic Zamolodchikov-Fateev hamiltonian with toroidal boundary conditions are given up to macroscopic momenta, by a Z(2) parafermion combined with a free boson. We show how to project out from this spectra various N = 1 superconformal systems. We give the operator content corresponding to the various sectors of these systems determined by internal symmetries and boundary conditions. In particular we recover all the modular invariants of Cappelli in two different ways. We next apply the same projection mechanism to finite chains. This is possible due to some special symmetry properties of the finite chains. In this way we get the spectra of various systems. In particular the spectra of the tricritical Ising model (c = 7 10 ) obtained from the spin-one chain coincides with those obtained from the spectra of the spin-1/2 XXZ Heisenberg chain. Through a simple generalization the number of states for some higher SU(2) × SU(2)/SU(2) coset models are obtained.