Integrability in anyonic quantum spin chains via a composite height model

Abstract

Recently, properties of collective states of interacting non-Abelian anyons have attracted considerable attention. We study an extension of the ``golden chain model,'' where two- and three-body interactions are competing. Upon fine tuning the interaction, the model is integrable. This provides an additional integrable point of the model, on top of the integrable point, when the three-body interaction is absent. To solve the model, we construct a new, integrable height model, in the spirit of the restricted solid-on-solid model solved by Andrews et al. [J. Stat. Phys. 35, 193 (1984)]. The heights in our model live on both the sites and links of the square lattice. The model is solved by means of the corner transfer matrix method. We find a connection between local height probabilities and characters of a conformal field theory governing the critical properties at the integrable point. In the antiferromagnetic regime, the criticality is described by the ${Z}_{k}$ parafermion conformal field theory, while the $\frac{\text{su}{(2)}_{1}\ifmmode\times\else\texttimes\fi{}\text{su}{(2)}_{1}\ifmmode\times\else\texttimes\fi{}\text{su}{(2)}_{k\ensuremath{-}2}}{\text{su}{(2)}_{k}}$ coset conformal field theory describes the ferromagnetic regime.