Integrable anyon chains: from fusion rules to face models to effective field theories

TL;DR

This paper constructs and analyzes integrable one-dimensional anyon lattice models based on $SO(5)_2$ fusion rules, revealing their critical behavior and conformal field theory descriptions through Bethe ansatz and finite size spectrum analysis.

Contribution

It introduces new integrable anyon chain models from $SO(5)_2$ fusion rules and connects their low-energy behavior to specific rational conformal field theories.

Findings

Two models are critical at zero temperature.

Models are described by $ ext{W}B_2$ and $ ext{W}D_5$ conformal field theories.

Modular partition functions and fusion rules match lattice model results.

Abstract

Starting from the fusion rules for the algebra $SO(5)_2$ we construct one-dimensional lattice models of interacting anyons with commuting transfer matrices of `interactions round the face' (IRF) type. The conserved topological charges of the anyon chain are recovered from the transfer matrices in the limit of large spectral parameter. The properties of the models in the thermodynamic limit and the low energy excitations are studied using Bethe ansatz methods. Two of the anyon models are critical at zero temperature. From the analysis of the finite size spectrum we find that they are effectively described by rational conformal field theories invariant under extensions of the Virasoro algebra, namely $\mathcal{W}B_2$ and $\mathcal{W}D_5$, respectively. The latter contains primaries with half and quarter spin. The modular partition function and fusion rules are derived and found to be consistent with the results for the lattice model.