Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way

Abstract

A family of two-dimensional (2D) spin-1/2 models have been constructed to realize Kitaev's sixteen-fold way of anyon theories. Defining a one-dimensional (1D) path through all the lattice sites, and performing the Jordan-Wigner transformation with the help of the 1D path, we find that such a spin-1/2 model is equivalent to a model with $\nu$ species of Majorana fermions coupled to a static ${\mathbb{Z}}_2$ gauge field. Here each specie of Majorana fermions gives rise to an energy band that carries a Chern number $\mathcal{C}=1$, yielding a total Chern number $\mathcal{C}=\nu$. It has been shown that the ground states are three (four)-fold topologically degenerate on a torus, when $\nu$ is an odd (even) number. These exactly solvable models can be achieved by quantum simulations.

arXiv comment20 pages, 9 figures

References in corpus (36)

• Anyons in an exactly solved model and beyond
• Quantum Spin Liquids
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum Spin Liquid States
• Quantum Spin Liquids
• Zoo of quantum-topological phases of matter
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Anyons and the quantum Hall effect - a pedagogical review
• The Flux-Phase of the Half-Filled Band
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Vaporization of Kitaev spin liquids
• Exactly solvable Kitaev model in three dimensions
• Classification of gapless Z2 spin liquids in three-dimensional Kitaev models
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Algebraic spin liquid in an exactly solvable spin model
• Quantum order from string-net condensations and origin of light and massless fermions
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Weyl spin liquids
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Mosaic spin models with topological order
• A $\Gamma$-matrix generalization of the Kitaev model
• Three-dimensional topological phase on the diamond lattice
• Toward Kitaev's sixteenfold way in a honeycomb lattice model
• Quantum spin metal state on a decorated honeycomb lattice
• Kaleidoscope of topological phases with multiple Majorana species
• Topological phase transitions driven by gauge fields in an exactly solvable model
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way
• Exact quantum spin liquids with Fermi surfaces in spin-half models
• Exactly soluble spin-1/2 models on three-dimensional lattices and non-abelian statistics of closed string excitations
• Pristine Mott Insulator from an Exactly Solvable Spin-1/2 Kitaev Model

Cited by in corpus (2)

• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality