Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model

Abstract

The spectral properties of Kitaev's honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the $2^n$-fold ground state degeneracy in the presence of $2n$ well separated vortices and the lifting of the degeneracy due to their short-range interactions. The calculations are performed on an infinite lattice. In addition to the analytic treatment, a numerical study of finite size systems is performed which is in exact agreement with the theoretical considerations. The general spectral properties of the non-abelian phase are considered for various finite toroidal systems.

32 pages, 13 figures; corrected typos and changed SU(2)_2 to Ising

References in corpus (6)

• A toolbox for lattice spin models with polar molecules
• An exact chiral spin liquid with non-Abelian anyons
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Zero modes of two-dimensional chiral p-wave superconductors
• An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase

Cited by in corpus (50)

• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Tunneling of anyonic Majorana excitations in topological superconductors
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Physical solutions of the Kitaev honeycomb model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Fidelity in topological quantum phases of matter
• STM as a single Majorana detector of Kitaev's chiral spin liquid
• Splitting the Topological Degeneracy of non-Abelian Anyons
• Vortex structures and zero energy states in the BCS-to-BEC evolution of p-wave resonant Fermi gases
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Perturbed vortex lattices and the stability of nucleated topological phases
• Splitting and oscillation of Majorana zero modes in the p-wave BCS-BEC evolution with plural vortices
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Anyonic entanglement renormalization
• Kaleidoscope of topological phases with multiple Majorana species
• Interacting Anyonic Fermions in a Two-Body Color Code Model
• Topological phase transitions driven by gauge fields in an exactly solvable model
• Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings
• Non-abelian statistics from an abelian model
• Topological quantum phase transition in an extended Kitaev spin model
• Tunable Splitting of the Ground-State Degeneracy in 1D Parafermionic Wires
• Kitaev model and dimer coverings on the honeycomb lattice
• Kitaev spin models from topological nanowire networks
• An exactly soluble model with tunable p-wave paired fermion ground states
• Seeing Majorana fermions in time-of-flight images of spinless fermions coupled by s-wave pairing
• Zero energy and chiral edge modes in a p-wave magnetic spin model
• Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way
• Analytic calculation of the vison gap in the Kitaev spin liquid
• A complete characterization of the spectrum of the Kitaev model on spin ladders
• Geometric description of the Kitaev honeycomb lattice model
• Non-locality of non-Abelian anyons
• Finite temperature geometric properties of the Kitaev honeycomb model
• Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field
• Vortex Loops and Majoranas
• Anyonic Quantum Walks
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• An anyon model in a toric honeycomb lattice
• Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Geometric phase through spatial potential engineering
• Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids
• The Kekulé-Kitaev model: linear and non-linear responses and magnetic field effects
• Flux-induced midgap states between strain-engineered flat bands