Operator content of the Ashkin-Teller quantum chain, superconformal and Zamolodchikov-Fateev invariance. I. Free boundary conditions

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.

[1]  M. Baake,et al.  Operator content of the Ashkin-Teller quantum chain, superconformal and Zamolodchikov-Fateev invariance. II. Boundary conditions compatible with the torus , 1987 .

[2]  V. Rittenberg,et al.  The Ashkin-teller Quantum Chain and Conformal Invariance , 1987 .

[3]  V. Rittenberg,et al.  Superconformal invariance in the Ashkin-Teller quantum chain with free boundary conditions , 1986 .

[4]  J. Cardy.  Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories , 1986 .

[5]  V. Rittenberg,et al.  The spectra of quantum chains with free boundary conditions and Virasoro algebras , 1986 .

[6]  A. Kent,et al.  Determinant Formulae and Unitarity for the N=2 Superconformal Algebras in Two-Dimensions or Exact Results on String Compactification , 1986 .

[7]  G. Waterson.  Bosonic Construction of an $N=2$ Extended Superconformal Theory in Two-dimensions , 1986 .

[8]  E. Corrigan.  Twisted vertex operators and representations of the Virasoro algebra , 1986 .

[9]  Adrian Kent,et al.  Unitary representations of the Virasoro and super-Virasoro algebras , 1986 .

[10]  P. Vecchia,et al.  N=2 Extended Superconformal Theories in Two-Dimensions , 1985 .

[11]  V. G. Knizhnik,et al.  Superconformal symmetry in two dimensions , 1985 .

[12]  H. Eichenherr.  Minimal operator algebras in superconformal quantum field theory , 1985 .

[13]  S. Shenker,et al.  Superconformal invariance in two dimensions and the tricritical Ising model , 1985 .

[14]  J. Cardy,et al.  Conformal Invariance and Surface Critical Behavior , 1984 .

[15]  J. Ashkin,et al.  Two Problems in the Statistical Mechanics of Crystals. I. The Propagation of Order in Crystal Lattices. I. The Statistics of Two-Dimensional Lattices with Four Components. , 1943 .