Kaleidoscope of topological phases with multiple Majorana species

Abstract

Exactly solvable lattice models for spins and non-interacting fermions provide fascinating examples of topological phases, some of them exhibiting the localized Majorana fermions that feature in proposals for topological quantum computing. The Chern invariant $\nu$ is one important characterization of such phases. Here we look at the square-octagon variant of Kitaev's honeycomb model. It maps to spinful paired fermions and enjoys a rich phase diagram featuring distinct abelian and nonabelian phases with $\nu =0,\pm 1,\pm 2,\pm 3$ and $\pm 4$. The $\nu =\pm 1$ and $\nu =\pm 3$ phases all support localized Majorana modes and are examples of Ising and $SU(2{)}_2$ anyon theories respectively.

6 pages, 5 figures. The second version has a new title, reflecting a change of focus of the presentation in this version. The third version contains minor changes and is essentially the one published in New Journal of Physics

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Andreev reflection from non-centrosymmetric superconductors and Majorana bound state generation in half-metallic ferromagnets
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• A $\Gamma$-matrix generalization of the Kitaev model
• Three-dimensional topological phase on the diamond lattice
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• The Wavefunction of an Anyon
• Superconducting phase with a chiral $f$-wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor
• An exactly soluble model with tunable p-wave paired fermion ground states
• Zero energy and chiral edge modes in a p-wave magnetic spin model

Cited by in corpus (24)

• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
• Toward Kitaev's sixteenfold way in a honeycomb lattice model
• Low-energy sub-gap states in multi-channel Majorana wires
• Perturbed vortex lattices and the stability of nucleated topological phases
• Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• An exactly solvable BCS-Hubbard Model in arbitrary dimensions
• Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• The modular S-matrix as order parameter for topological phase transitions
• Kitaev spin models from topological nanowire networks
• Focus on topological quantum computation
• Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way
• Generic Field-Driven Phenomena in Kitaev Spin Liquids: Canted Magnetism and Proximate Spin Liquid Physics
• Field stability of Majorana spin liquids in antiferromagnetic Kitaev models
• Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Exactly solvable model of topological insulator realized on spin-1/2 lattice
• Edge Theories for Anyon Condensation Phase Transitions
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
• Inverse Hamiltonian design of highly-entangled quantum systems