An exact chiral spin liquid with non-Abelian anyons

by Hong Yao, Steven A. Kivelson

This is another interesting development in the field of topological quantum computing that came out during the Aspen work shop on the subject this summer. In the Kitaev model, a bizarre but exactly solvable spin model on the honeycombe lattice, a topological phase with non-abelian topological defects (vortices) can arise in the presence of a magnetic field. Unfortunately, a magnetic field spoils the exact solvability of the model leaving us only with a perturbative understanding of this interesting phase.

Here, Yao and Kivelson extend the Kitaev model to a lattice that is somewhere in between a honeycombe and a kagome lattice. They show that the topological phase with non-abelian excitations can arise spontaneously in this extended model. Furthermore, they were able to analyse the phase exactly. In addition, they make use of a recent discovery by Feng, Zhang and Xiang who solved the Kitaev model by a simple Jordan-Wigner transformation which converts the model into spinless fermions that in turn reduces to a model of free Marajona (charge neutral) fermions. As a result, Yao and Kivelson are able to explain their results in a very simple and intuitive language.