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.

34 pages, 5 figures; v2: expanded introduction, references added and other minor changes

References in corpus (9)

• Interacting anyons in topological quantum liquids: The golden chain
• Condensate induced transitions between topologically ordered phases
• A theory of topological edges and domain walls
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Collective states of interacting Fibonacci anyons
• The $Z_2$ staggered vertex model and its applications
• Corner transfer matrices in statistical mechanics
• Integrability in anyonic quantum spin chains via a composite height model
• Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization