Generalized Kitaev Models and Extrinsic Non-Abelian Twist Defects

Maissam Barkeshli, Hong-Chen Jiang, Ronny Thomale, and Xiao-Liang Qi

Phys. Rev. Lett. 114, 026401 – Published 13 January 2015

Abstract

We present a wide class of partially integrable lattice models with two-spin interactions which generalize the Kitaev honeycomb model. These models have a conserved quantity associated with each plaquette, conserved large loop operators on the torus, and topological degeneracy. We introduce a “slave-genon” approach which generalizes the Majorana fermion approach in the Kitaev model. The Hilbert space of our spin model can be embedded in an enlarged Hilbert space of non-Abelian twist defects, referred to as genons. In the enlarged Hilbert space, the spin model is exactly reformulated as a model of non-Abelian genons coupled to a discrete gauge field. We discuss in detail a particular $Z_{3}$ generalization, and we show that in a certain limit the model is analytically tractable and produces a non-Abelian topological phase with chiral parafermion edge states.

Received 12 June 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.026401

Authors & Affiliations

Maissam Barkeshli¹, Hong-Chen Jiang^2,3, Ronny Thomale⁴, and Xiao-Liang Qi⁵

¹Microsoft Station Q, Santa Barbara, California 93106, USA
²Department of Physics, University of California, Berkeley, California 94720, USA
³Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
⁴Institute for Theoretical Physics, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany
⁵Department of Physics, Stanford University, Stanford, California 94305, USA