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

2008/04/30 by Sébastien Dusuel, S. Dusuel, K. P. Schmidt +5 · 6 citations
Mathematics · Physics and Astronomy · #Abelian group #Advanced Condensed Matter Physics #Combinatorics #Ground state #Lattice (music) #Limit (mathematics) #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Spin model #Symmetry breaking #Theoretical physics #Topological quantum computer #cond-mat.other #quant-ph

paper · pdf · doi:10.1103/physrevb.78.125102

published as Phys. Rev. B 78, 125102 (2008) · 7 pages, 4 figures, published version

openalex publication_date 2008/09/05 · arxiv created 2008/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 multiplaquette 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.

Citations

• On the theory of identical particles
• Exact Results for Quench Dynamics and Defect Production in a Two-Dimensional Model
• Spectrum of the non-abelian phase in Kitaev’s honeycomb lattice model
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Anyonic interferometry and protected memories in atomic spin lattices
• Flow‐equations for Hamiltonians

Cited by

• Kitaev model and dimer coverings on the honeycomb lattice
• Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Quantum spin liquid states
• Spin-12 Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks
• Edge states and topological orders in the spin liquid phases of star lattice

Related

• An exact chiral spin liquid with non-Abelian anyons
• Phase Diagram of the Kitaev-type Model on a Decorated Honeycomb Lattice in the Isolated Dimer Limit
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Assembling Kitaev honeycomb spin liquids from arrays of 1D symmetry protected topological phases