Toward Kitaev's sixteenfold way in a honeycomb lattice model

TL;DR

This paper realizes and classifies multiple topological orders in a honeycomb lattice model, expanding understanding of Kitaev's sixteenfold way and identifying potential experimental signatures.

Contribution

It explicitly constructs several topological phases within Kitaev's sixteenfold way in an exactly solvable honeycomb model, identifying their anyonic excitations and symmetries.

Findings

Realized topological orders with Chern numbers 0, ±1, ±2, ±3, ±4, ±8

Identified anyonic excitations and confirmed their properties

Observed potential weak supersymmetry in anyon spectrum

Abstract

Kitaev's sixteenfold way is a classification of exotic topological orders in which $\mathbb{Z}_2$ gauge theory is coupled to Majorana fermions of Chern number $C$. The $16$ distinct topological orders within this class, depending on $C \, \mathrm{mod} \, 16$, possess a rich variety of Abelian and non-Abelian anyons. We realize more than half of Kitaev's sixteenfold way, corresponding to Chern numbers $0$, $\pm 1$, $\pm 2$, $\pm 3$, $\pm 4$, and $\pm 8$, in an exactly solvable generalization of the Kitaev honeycomb model. For each topological order, we explicitly identify the anyonic excitations and confirm their topological properties. In doing so, we observe that the interplay between lattice symmetry and anyon permutation symmetry may lead to a "weak supersymmetry" in the anyon spectrum. The topological orders in our honeycomb lattice model could be directly relevant for honeycomb Kitaev materials, such as $\alpha$-RuCl$_3$, and would be distinguishable by their specific quantized values of the thermal Hall conductivity.