An anyon model in a toric honeycomb lattice

TL;DR

This paper introduces a new anyon model on a toric honeycomb lattice, revealing its relation to the Kitaev toric code, and connects it to boundary-coupled Ising chains, enhancing understanding of anyonic systems in symmetric and fermionic frameworks.

Contribution

It presents a novel honeycomb lattice anyon model, establishes its equivalence to the Kitaev toric code, and links it to boundary Ising chains through Jordan-Wigner transformation.

Findings

Ground states match Kitaev toric code

Excitations obey mutual semionic statistics

Model can be realized in fermionic systems

Abstract

We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan-Wigner transformation. We discuss the equivalence between these two models in the low-lying sector and realize these anyon excitations in a conventional fermion system.