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Physical Review Letters

Generalized parafermionic theory and integrable lattice models

Marcio Jose Martins

Published Oct 22, 1990• 22 citations
Publisher

Abstract

We show that the criticality of integrable lattice models based on the Lie algebras ${\mathit{A}}_{\mathit{n}}$,${\mathit{D}}_{\mathit{n}}$,${\mathit{E}}_{\mathit{n}}$ can be understood as the product of certain numbers of bosonic fields and a generalized parafermionic (fractional spin) theory (GPT). We compute the central charge of the GPT using the thermodynamic Bethe-ansatz approach. For the model associated with the ${\mathit{A}}_{2}$ Lie algebra, we propose that the associated GPT can be described by a composition of Ising and tricritical-Ising conformal field theories.

DOI
10.1103/physrevlett.65.2091

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We derive the fusion hierarchy of functional equations for critical A-D-E lattice models related to the sℓ ( 2 ) unitary minimal models, the parafermionic models and the supersymmetric models of conformal field theory and deduce the related TBA functional equations. The derivation uses fusion projectors and applies in the presence of all known integrable boundary conditions on the torus and cylinder. The resulting TBA functional equations are universal in the sense that they depend only on the Coxeter number of the A-D-E graph and are independent of the particular integrable boundary conditions. We conjecture generally that TBA functional equations are universal for all integrable lattice models associated with rational CFTs and their integrable perturbations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.