Honeycomb lattice Kitaev model with Wen-Toric-code interactions, and anyon excitations

Abstract

The honeycomb lattice Kitaev model H_{K} with two kinds of Wen-Toric-code four-body interactions H_{WT} is investigated exactly using a new fermionization method, and the ground state phase diagram is obtained. Six kinds of three-body interactions are also considered. A Hamiltonian equivalent to the honeycomb lattice Kitaev model is also introduced. The fermionization method is generalized to two-dimensional systems, and the two-dimensional Jordan-Wigner transformation is obtained as a special case of this formula. The model H_{K}+H_{WT} is symmetric in four-dimensional space of coupling constants, and the anyon type excitations appear in each phase.

arXiv comment23 pages, 10 figures

References in corpus (13)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Quantum orders in an exact soluble model
• The Flux-Phase of the Half-Filled Band
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• The Bond-Algebraic Approach to Dualities
• Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities
• Topological quantum phase transition in an extended Kitaev spin model
• An exactly soluble model with tunable p-wave paired fermion ground states
• Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
• Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

Cited by in corpus (9)

• Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator
• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
• Geometric Criterion for Solvability of Lattice Spin Systems
• Exact solution of a cluster model with next-nearest-neighbor interaction
• Onsager algebra and algebraic generalization of Jordan-Wigner transformation
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• Conserved Charges of Series of Solvable Lattice Models
• The exact susceptibility of the spin-S transverse Ising chain with next-nearest-neighbor interactions
• Towards Yang-Baxter integrability of quantum crystal melting: From Kagome lattice to vertex models