Local height probabilities in a composite Andrews–Baxter–Forrester model

Abstract

We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two-and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behaviour of the composite height model, the critical behaviour of the anyonic chains is established as well. Depending on the overall sign of the hamiltonian, this critical behaviour is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.

Anyonic quantum spin chains: Spin-1 generalizations and topological stability

“…One of the integrable points identified in 40 corresponds to the supersymmetric critical point forming the boundary of the Haldane phase. The location of this integrable point, in terms of the parameters used in this paper, is tan θ 2,1 = − 1 2 d1+1 d1 , where d 1 = 1 + 2 cos (2π/(k + 2)) (see 53 ). For k ≥ 4, this location depends only weakly on k, namely, for k = 4, one obtains θ 2,1 = − arctan(3/4) ≈ −0.2048π, while in the limit k → ∞, one obtains θ 2,1 = − arctan(2/3) ≈ −0.1872π.…”

“…To solve the anyonic spin-1 chain at this integrable point, one approach is to map the model to a fused RSOS model, as studied in 23,54 (see also 55,56). This subject will be described in a separate publication 53 .…”