Integrability in anyonic quantum spin chains via a composite height model

TL;DR

This paper introduces an integrable height model for non-abelian anyon chains, revealing new critical points and connecting local height probabilities to conformal field theories, with solutions obtained via the corner transfer matrix method.

Contribution

It constructs a novel integrable height model for anyonic chains, extending the golden chain model and linking its critical behavior to specific conformal field theories.

Findings

Identification of an integrable point with fine-tuned interactions.

Connection of height probabilities to conformal field theory characters.

Description of critical regimes by Z_k parafermion and coset conformal field theories.

Abstract

Recently, properties of collective states of interacting non-abelian anyons have attracted a 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, Baxter and Forrester. 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 su(2)_1 x su(2)_1 x su(2)_(k-2) / su(2)_k coset conformal field theory describes the ferromagnetic regime.