Generalized Kitaev Models and Slave Genons

Abstract

We present a wide class of partially integrable lattice models with two-spin interactions, which generalize the Kitaev honeycomb model. These models have an infinite number of conserved quantities associated with each plaquette of the lattice, conserved large loop operators on the torus, and protected topological degeneracy. We introduce a `slave-genon' approach, which generalizes the Majorana fermion approach in the Kitaev honeycomb model. The Hilbert space of our spin model can be embedded into 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 show that in a certain limit the model is analytically tractable and may produce a non-Abelian topological phase with chiral parafermion edge states.

5 pages main text + 8 pages appendix

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Interacting anyons in topological quantum liquids: The golden chain
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Fractional topological superconductors with fractionalized Majorana fermions
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• $Z_3$ generalization of the Kitaev's spin-1/2 model

Cited by in corpus (8)

• Parafermionic conformal field theory on the lattice
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Criticality in Translation-Invariant Parafermion Chains
• Symmetry Enrichment in Three-Dimensional Topological Phases
• General phase spaces: from discrete variables to rotor and continuum limits
• Pretopological fractional excitations in the two-leg flux ladder
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit