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Journal of Physics A Mathematical and General

The operator content of the ferromagnetic and antiferromagnetic spin-1 Zamolodchikov-Fateev quantum chain

D. Baranowski, V. Rittenberg

Published Mar 21, 1990• 16 citations
Publisher

Abstract

The finite-size scaling spectra of the spin-1 Zamolodchikov-Fateev chain for an even and odd number of sites are presented. The operator content is given for free as well as toroidal boundary conditions. In the case of the antiferromagnetic chain the authors give separately the ferromagnetic and antiferromagnetic excitations.
DOI
10.1088/0305-4470/23/6/023

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Based on numerical analysis, the authors conjecture the operator content of the finite-size limit of the spectra of the Ashkin-Teller model with free boundary conditions. The same operator content is obtained from a Hamiltonian with a four-fermion interaction and a U(1) Kac-Moody Sugawara structure. For some special values of the coupling constant the model exhibits N=2 superconformal and Zamolodchikov-Fateev invariance. The operator content in these cases is expressed in terms of irreducible representations of the corresponding algebras.
The sector of zero ZN charge is studied for the ferromagnetic (FM) and antiferromagnetic (AFM) version of the (ZN×Z2)-invariant Fateev-Zamolodchikov quantum spin chain. We conjecture that the relevant Bethe ansatz equations should admit, besides the usual stringlike solutions, exceptional multiplets, and a number of nonphysical solutions. Once the physical ones are identified, we show how completeness and the gapless excitation spectrum can be obtained. The central charge is computed from the specific heat and found to be [Formula: see text] (FM) and c=1 (AFM).
For pt. I, see ibid., vol. 20, no.8, p.L479-85 (1987). The authors present the operator content of the Ashkin-Teller quantum chain with eight boundary conditions corresponding to the eight elements of the group D 4 which gives the global symmetry of the system. This operator content is a conjecture based on an extensive numerical study and was proven to be correct at the Ising decoupling point. For the values of the coupling constant where N=2, superconformal invariance was seen for free boundary conditions. The situation is now more complex. One finds sectors which have N=2 and N=1 superconformal invariance and sectors which have no superconformal invariance at all. If, however, they combine the 'wrong' sectors of the spectra which correspond to two different values of the coupling constant, a new symmetry shows up. They also analyse the operator content at the Fateev-Zamolodchikov points. Here the 'wrong' sectors can be described by a few new primary fields.
The authors derive the operator content of the spin-S XXZ quantum chain with generalised toroidal boundary conditions compatible with the U(1) symmetry of the model. These results are derived by solving numerically the associated Bethe ansatz equations for finite chains and exploring the consequences of the conformal invariance of the infinite system. They also show that, as in the spin-1/2 case, the conformal anomaly and dimensions of general extended SU(2) algebras can be obtained from these spin-S chains by choosing properly the coupling constant and the boundary condition.