Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking

Abstract

We analyze the Kitaev model on the triangle-honeycomb lattice whose ground state has recently been shown to be a chiral spin liquid. We consider two perturbative expansions: the isolated-dimer limit containing Abelian anyons and the isolated-triangle limit. In the former case, we derive the low-energy effective theory and discuss the role played by multi-plaquette interactions. In this phase, we also compute the spin-spin correlation functions for any vortex configuration. In the isolated-triangle limit, we show that the effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at the isotropic point. We also compute the next-order correction which opens a gap and yields non-Abelian anyons.

7 pages, 4 figures, published version

References in corpus (10)

• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Exact results for quench dynamics and defect production in a two-dimensional model
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Anyonic interferometry and protected memories in atomic spin lattices
• Emergent Fermions and Anyons in the Kitaev Model
• Shot Noise in Anyonic Mach-Zehnder Interferometer
• Creation and Manipulation of Anyons in the Kitaev Model

Cited by in corpus (4)

• A $\Gamma$-matrix generalization of the Kitaev model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Fidelity in topological quantum phases of matter
• The Zero Temperature Phase Diagram of the Kitaev Model