Quantum and classical behavior of spin-$S$ Kitaev models in an anisotropic limit

Abstract

We study low-energy properties of spin-$S$ Kitaev models in an anisotropic limit. The effective form of a local conserved quantity is derived in the low-energy subspace. We find this is the same as that of $S=1/2$ case for the half-integer spins but shows a different form for the integer spins. Applying the perturbation theory to the anisotropic Kitaev model, we obtain the effective Hamiltonian. In the integer spin case, the effective model is equivalent to a free spin model under an uniform magnetic field, where quantum fluctuations are quenched. On the other hand, in the half-integer case, the system is described by the toric code Hamiltonian, where quantum fluctuations play a crucial role in the ground state. The boundary effect in the anisotropic Kitaev system is also discussed.

arXiv comment8 pages, 7 figures

References in corpus (70)

• Fault-tolerant quantum computation by anyons
• 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
• Quantum Spin Liquids
• 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
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• 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
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Evidence for a Field-induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• 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
• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
• Fermionic response from fractionalization in an insulating two-dimensional magnet
• Spin-orbit excitation energies, anisotropic exchange, and magnetic phases of honeycomb RuCl3
• A new spin-anisotropic harmonic honeycomb iridate
• Phase Diagram of $\alpha$-RuCl${}_3$ in an in-plane Magnetic Field
• 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
• Na2IrO3 as a spin-orbit-assisted antiferromagnetic insulator with a 340 meV gap
• Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Anisotropic Ru3+ 4d5 magnetism in the alpha-RuCl3 honeycomb system: susceptibility, specific heat and Zero field NMR
• Unusual thermal Hall effect in a Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Vaporization of Kitaev spin liquids
• Anomalous thermal conductivity and magnetic torque response in the honeycomb magnet $\alpha$-RuCl${}_3$
• Large field-induced gap of Kitaev-Heisenberg paramagnons in $\alpha$-RuCl${}_3$
• Field-induced quantum criticality in the Kitaev system $\alpha$-RuCl${}_3$
• Magnetic Excitations and Continuum of a Field-Induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Topological Magnons in Kitaev Magnets at High Fields
• Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
• Observation of two types of anyons in the Kitaev honeycomb magnet
• Thermal Transport in the Kitaev Model
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Robust non-Abelian spin liquid and possible intermediate phase in antiferromagnetic Kitaev model with magnetic field
• Dynamical and Topological Properties of the Kitaev Model in a [111] Magnetic Field
• Fractional Spin Fluctuation as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
• Topological excitations in the ferromagnetic Kitaev-Heisenberg model
• Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na${}_2$IrO${}_3$
• Heisenberg-Kitaev model on hyperhoneycomb lattice
• Emergent Fermions and Anyons in the Kitaev Model
• Ultralow-temperature thermal conductivity of the Kitaev honeycomb magnet $\alpha$-RuCl${}_3$ across the field-induced phase transition
• Unconventional spin dynamics in the honeycomb-lattice material $\alpha$-RuCl${}_3$: high-field ESR studies
• 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
• Global phase diagram of a doped Kitaev-Heisenberg model
• Ground-state and thermodynamic properties of an $S=1$ Kitaev model
• Comprehensive study of the dynamics of a classical Kitaev spin liquid
• Dirac and Chiral Quantum Spin Liquids on the Honeycomb Lattice in a Magnetic Field
• Incipient and well-developed entropy plateaus in spin-S Kitaev models
• Intermediate gapless phase and topological phase transition of Kitaev model in a uniform magnetic field
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Spin Chains with Periodic Array of Impurities
• Quantum spin liquid in the semiclassical regime
• Effective actions for spin ladders
• Alternating spin chains with singlet ground states
• Interlayer Coupling Effect on a Bilayer Kitaev Model
• Mixed-Spin Ladders and Plaquette Spin Chains
• Frustration-induced phase transitions in the spin-S orthogonal-dimer chain
• Role of the spin-orbit coupling in the Kugel-Khomskii model on the honeycomb lattice

Cited by in corpus (21)

• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Magnetic Field Induced Spin Liquids in S=1 Kitaev Honeycomb Model
• Majorana-mediated spin transport without spin polarization in Kitaev quantum spin liquids
• Learning Quantum Hamiltonians from Single-qubit Measurements
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• ${\mathbb{Z}}_2$ spin liquids in the higher spin-$S$ Kitaev honeycomb model: An exact deconfined ${\mathbb{Z}}_2$ gauge structure in a non-integrable model
• Excitation spectrum of spin-1 Kitaev spin liquids
• Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies
• Low temperature properties in the Bilayer Kitaev model
• Residual Entropy and Spin Fractionalizations in the Mixed-Spin Kitaev Model
• Spin transport in the Quantum Spin Liquid State in the $S=1$ Kitaev model: role of the fractionalized quasiparticles
• Insights into the Anisotropic Spin-$S$ Kitaev Chain
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• State selection in frustrated magnets
• Phase diagrams of spin-$S$ Kitaev ladders
• Order by singularity in Kitaev clusters
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice
• Magnetic properties of the S = 1 Kitaev model with anisotropic interactions