Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state

Abstract

We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with $Z_2$ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the ${\Gamma }^{\prime }$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction, and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\pm 1$ to an Abelian phase with the Chern number equal to $\pm 2$, in which the $Z_2$ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\Gamma$ term, only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.

arXiv comment8 pages, 7 figures

References in corpus (48)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Low-temperature crystal and magnetic structure of $\alpha$-RuCl3
• Direct evidence of a zigzag spin chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation on single crystal $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$
• Evidence for a Field-induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Crystal structure and magnetism in $\alpha$-RuCl3: an ab-initio study
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Gapless Spin Excitations in the Field-Induced Quantum Spin Liquid Phase of alpha-RuCl3
• Spin-wave excitations evidencing the Kitaev interaction in single crystalline $\alpha$-RuCl${}_3$
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Unusual thermal Hall effect in a Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Large field-induced gap of Kitaev-Heisenberg paramagnons in $\alpha$-RuCl${}_3$
• Incommensurate Counterrotating Magnetic Order Stabilized by Kitaev Interactions in the Layered Honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Kitaev-Heisenberg-J2-J3 model for the iridates A2IrO3
• Emergence of a Field-Driven U(1) Spin Liquid in the Kitaev Honeycomb Model
• Observation of two types of anyons in the Kitaev honeycomb magnet
• Dynamics of the Kitaev-Heisenberg Model
• Thermal Transport in the Kitaev Model
• Theoretical investigation of the magnetic dynamics in $\alpha$-RuCl${}_3$
• Quantization of the thermal Hall conductivity at small Hall angles
• Theory of the field-revealed Kitaev spin liquid
• Robust non-Abelian spin liquid and possible intermediate phase in antiferromagnetic Kitaev model with magnetic field
• Low-energy Spin Dynamics of the Honeycomb Spin Liquid Beyond the Kitaev Limit
• Approximately quantized thermal Hall effect of chiral liquids coupled to phonons
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets
• Toward Kitaev's sixteenfold way in a honeycomb lattice model
• Impact of off-diagonal exchange interactions on the Kitaev spin liquid state of $\alpha$-RuCl${}_3$
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Field-induced quantum spin liquid in the Kitaev-Heisenberg model and its relation to $\alpha$-RuCl${}_3$
• Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces
• Majorana-mediated spin transport without spin polarization in Kitaev quantum spin liquids
• Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice
• Vison-Majorana complex zero-energy resonance in Kitaev's spin liquid
• Nonequilibrium Majorana Dynamics by Quenching a Magnetic Field in Kitaev Spin Liquids
• Ground state properties of $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ determined from $\text{ab initio}$ Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions
• Trigonal distortion in the honeycomb iridates: Proximity of zigzag and spiral phases in Na2IrO3

Cited by in corpus (12)

• STM as a single Majorana detector of Kitaev's chiral spin liquid
• Linear and Nonlinear Optical Responses in Kitaev Spin Liquids
• Electric-field control of magnetic anisotropies: applications to Kitaev spin liquids and topological spin textures
• Counterdiabatic route for preparation of state with long-range topological order
• Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid
• Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields
• Interplay of magnetic field and trigonal distortion in the honeycomb $\Gamma$ model: Occurrence of a spin-flop phase
• Field-driven spatiotemporal manipulation of Majorana zero modes in a Kitaev spin liquid
• Electric probe for the toric code phase in Kitaev materials through the hyperfine interaction
• Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation
• Tuning the Chern number of Kitaev quantum spin liquid
• Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid