Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation

Abstract

Quantum spin liquids realized in the Kitaev model offer a platform for fractionalization of spin into two quasiparticles: itinerant Majoranas and localized visons. Introducing a uniform weak magnetic field associates a Majorana zero mode with each vison excitation. The vison accompanied by a Majorana zero mode is known to behave as a non-Abelian anyon, which has garnered significant attention for its potential applications in topological quantum computing. Although spatial and temporal control of these anyons is essential for exploring their applicability in quantum computing, numerical simulations of creating, moving, and annihilating anyons by an external field remain challenging as this field violates the exact solvability of the Kitaev model. Moreover, such a field to control anyons may disturb the quantum state due to the energy injection it causes. In this study, by introducing energy dissipation phenomenologically in real-time simulations, we demonstrate that the generation, movement, and annihilation of vison excitations can be achieved while maintaining their localization. We find that a vison can be moved in a desired direction by using time-dependent local magnetic fields or gradient fields, and it remains accompanied by a Majorana zero mode even after its movement. We also reveal that a larger spatial extent of the Majorana zero modes bound to a vison facilitates the movement of the vison with smaller field gradients. Furthermore, our numerical simulations demonstrate pair creation and annihilation of visons, triggered by time-dependent magnetic fields. The results obtained in this study highlight the significance of energy dissipation in controlling non-Abelian anyons, which will stimulate further investigations into the nonequilibrium dynamics of fractional quasiparticles in strongly correlated electron systems, as well as studies for applications in quantum computation.

arXiv comment20 pages, 12 figures

References in corpus (137)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Helical liquids and Majorana bound states in quantum wires
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Topological superconductors: a review
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Exponential Protection of Zero Modes in Majorana Islands
• 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
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Kitaev quantum spin liquid - concept and materialization
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• A short introduction to the Lindblad Master Equation
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• A Field Guide to Spin Liquids
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Observation of half-integer thermal Hall conductance
• Low-temperature crystal and magnetic structure of $\alpha$-RuCl3
• Majorana Fermions and Topology in Superconductors
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes
• Excitations in the field-induced quantum spin liquid state of alpha-RuCl3
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortex matter in a $p_x+i{p}_y$ superconductor
• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
• Fermionic response from fractionalization in an insulating two-dimensional magnet
• Breakdown of Magnons in a Strongly Spin-Orbital Coupled Magnet
• Hunting Majorana Fermions in Kitaev Magnets
• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Na2IrO3 as a spin-orbit-assisted antiferromagnetic insulator with a 340 meV gap
• Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Unusual thermal Hall effect in a Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Vaporization of Kitaev spin liquids
• Robustness of the thermal Hall effect close to half-quantization in a field-induced spin liquid state
• Theory of Anderson pseudospin resonance with Higgs mode in superconductors
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Dynamics of Fractionalization in Quantum Spin Liquids
• The planar thermal Hall conductivity in the Kitaev magnet α-RuCl3
• Observation of two types of anyons in the Kitaev honeycomb magnet
• Thermal Transport in the Kitaev Model
• Sample dependence of the half-integer quantized thermal Hall effect in the Kitaev candidate $\alpha$-RuCl${}_3$
• Quantum spin liquid signatures in Kitaev-like frustrated magnets
• Finite field regime for a quantum spin liquid in $\alpha$-RuCl${}_3$
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Topological phases in ultracold polar-molecule quantum magnets
• Low-energy Spin Dynamics of the Honeycomb Spin Liquid Beyond the Kitaev Limit
• Fractional Spin Fluctuation as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
• Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid Candidate $\alpha$-RuCl${}_3$
• Evidence for charge transfer and proximate magnetism in graphene/a-RuCl_3 heterostructures
• Spin-split band hybridization in graphene proximitized with $\alpha$-RuCl${}_3$ nanosheets
• Large Thermal Hall Effect in $\alpha$-RuCl${}_3$: Evidence for Heat Transport by Kitaev-Heisenberg Paramagnons
• Designing Kitaev spin liquids in metal-organic frameworks
• A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
• Thermodynamic evidence of fractionalized excitations in α-RuCl3
• Local Probes for Charge-Neutral Edge States in Two-Dimensional Quantum Magnets
• Antiferromagnetic Kitaev Interaction in $f$-Electron Based Honeycomb Magnets
• Magnetic thermal conductivity far above the Néel temperatures in the Kitaev-magnet candidate $\alpha$-RuCl${}_3$
• Successive Majorana Topological Transitions Driven by a Magnetic Field in the Kitaev Model
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Tunneling spectroscopy of quantum spin liquids
• Topological magnons for thermal Hall transport in frustrated magnets with bond-dependent interactions
• Kitaev honeycomb and other exotic spin models with polar molecules
• The range of non-Kitaev terms and fractional particles in RuCl${}_3$
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Phonon dynamics in the Kitaev spin liquid
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Heat capacity evidence for proximity to the Kitaev QSL in A${}_2$IrO${}_3$ ($A=$ Na, Li)
• Impact of off-diagonal exchange interactions on the Kitaev spin liquid state of $\alpha$-RuCl${}_3$
• Collective Modes in Excitonic Insulators: Effects of Electron-Phonon Coupling and Signatures in Optical Response
• STM as a single Majorana detector of Kitaev's chiral spin liquid
• Electrical Access to Ising Anyons in Kitaev Spin Liquids
• Dynamics of visons and thermal Hall effect in perturbed Kitaev models
• Floquet engineering in superconducting circuits: from arbitrary spin-spin interactions to the Kitaev honeycomb model
• Magnetism of Kitaev spin-liquid candidate material RuBr${}_3$
• Majorana dynamical mean-field study of spin dynamics at finite temperatures in the honeycomb Kitaev model
• Landau levels of Majorana fermions in a spin liquid
• Finite-Temperature Phase Transition to a Quantum Spin Liquid in a Three-Dimensional Kitaev Model on a Hyperhoneycomb Lattice
• Magnetic ordering with an XY-like anisotropy in the honeycomb lattice iridates ZnIrO${}_3$ and MgIrO${}_3$ synthesized via a metathesis reaction
• Phonon renormalization in the Kitaev quantum spin liquid
• Linear and Nonlinear Optical Responses in Kitaev Spin Liquids
• Majorana-mediated spin transport without spin polarization in Kitaev quantum spin liquids
• Bulk Photovoltaic Effect Driven by Collective Excitations in a Correlated Insulator
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
• Temperature evolution of spin dynamics in two- and three-dimensional Kitaev models: Influence of fluctuating gauge fluxes
• A quantum relaxation-time approximation for finite fermion systems
• Perspective: strain and strain gradient engineering in membranes of quantum materials
• Computational design of $f$-electron Kitaev magnets: honeycomb and hyperhoneycomb compounds $A_2$PrO${}_3$ ($A=$ alkali metals)
• Tunneling spectroscopy as a probe of fractionalization in 2D magnetic heterostructures
• Quantum Paraelectricity in the Kitaev Quantum-Spin-Liquid Candidates H${}_3$LiIr${}_2$O${}_6$ and D${}_3$LiIr${}_2$O${}_6$
• Strongly electron-correlated semimetal RuI${}_3$ with a layered honeycomb structure
• Phonon Thermal Hall Conductivity from Scattering with Collective Fluctuations
• Scanning tunneling spectroscopy of Majorana zero modes in a Kitaev spin liquid
• Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin structure factor, magnetic susceptibility, and NMR relaxation rate
• Vison-Majorana complex zero-energy resonance in Kitaev's spin liquid
• Investigation of the magnetoelastic coupling anisotropy in the Kitaev material $\alpha$-RuCl${}_3$
• Nonequilibrium Majorana Dynamics by Quenching a Magnetic Field in Kitaev Spin Liquids
• Field-angle dependence of thermal Hall conductivity in magnetically ordered Kitaev-Heisenberg system
• Non-local spin correlation as a signature of Ising anyons trapped in vacancies of the Kitaev spin liquid
• Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models
• Theory of electronic magnetoelectric coupling in $d^5$ Mott insulators
• Thermal Hall Effect in the Kitaev-Heisenberg System with Spin-Phonon Coupling
• Spin-Liquid--to--Spin-Liquid Transition in Kitaev Magnets Driven by Fractionalization
• Thermal anyon interferometry in phonon-coupled Kitaev spin liquids
• Electronic and magnetic properties of iridium ilmenites $A$IrO${}_3$ ($A=$ Mg, Zn, and Mn)
• Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state
• Analytic calculation of the vison gap in the Kitaev spin liquid
• Impurity-induced resonant spinon zero modes in Dirac quantum spin-liquids
• Dynamical anyon generation in Kitaev honeycomb non-Abelian spin liquids
• Thermal interferometry of anyons in spin liquids
• Defect-Induced Low-Energy Majorana Excitations in the Kitaev Magnet $\alpha$-RuCl${}_3$
• Electric-field control of magnetic anisotropies: applications to Kitaev spin liquids and topological spin textures
• Feasibility of Kitaev quantum spin liquids in ultracold polar molecules
• Phonon Dynamics in the Generalized Kitaev Spin Liquid
• Photoinduced collective mode, inhomogeneity, and melting in a charge order system
• Scattering phenomena for spin transport in Kitaev spin liquid
• Dynamics of fractionalized mean-field theories: consequences for Kitaev materials
• Stabilization of a honeycomb lattice of IrO${}_6$ octahedra in superlattices with ilmenite-type MnTiO${}_3$
• Field-driven spatiotemporal manipulation of Majorana zero modes in a Kitaev spin liquid
• Photocontrol of spin scalar chirality in centrosymmetric itinerant magnets
• Interedge spin resonance in the Kitaev quantum spin liquid
• Phonon Dynamics in the Chiral Kitaev Spin Liquid
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model

Cited by in corpus (1)

• Tunable anyonic permeability across ${\mathbb{Z}}_2$ spin liquid junctions