Anyon dynamics in field-driven phases of the anisotropic Kitaev model

Abstract

The Kitaev model on a honeycomb lattice with bond-dependent Ising interactions offers an exactly solvable model of a quantum spin liquid (QSL) with gapped $Z_2$ fluxes and gapless linearly dispersing Majorana fermions in the isotropic limit ($K_x=K_y=K_z$). We explore the phase diagram along two axes, an external magnetic field, $h$, applied out-of-plane of the honeycomb, and anisotropic interactions, $K_z$ larger than the other two. For $K_z/K\gg 2$ and $h=0$, the matter Majorana fermions have the largest gap, and the system is described by a gapped $Z_2$ Toric code in which the $Z_2$ fluxes form the low energy bosonic Ising electric (e) and magnetic (m) charges along with their fermionic bound state $\epsilon =e\times m$. In this regime, we find that a small out-of-plane magnetic field creates $\epsilon$ fermions that disperse in fixed one-dimensional directions before the transition to a valence bond solid phase, providing a direct dynamical signature of low energy $Z_2$ Abelian flux excitations separated from the Majorana sector. At lower $K_z$ in the center of the Abelian phase, in a regime we dub the primordial fractionalized (PF) regime, the field generates a hybridization between the $\epsilon$ fermions and the Majorana matter fermions, resulting in a $\psi$ fermion. All the other phases in the field-anisotropy plane are naturally obtained from this primordial soup. We show that in the $Z_2$ Abelian phase, including the PF regime, the dynamical structure factors of local spin flip operators reveal distinct peaks that can be identified as arising from different anyonic excitations. We present in detail their signatures in energy and momentum and propose their identification by inelastic light scattering or inelastic polarized neutron scattering as ``smoking gun" signatures of fractionalization in the QSL phase.

arXiv comment19 pages, 8 figures, 1 table

References in corpus (63)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Topological entanglement entropy
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Detecting topological order in a ground state wave function
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Quantum Orders and Symmetric Spin Liquids
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Chaos in quantum channels
• A Field Guide to Spin Liquids
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Low-temperature crystal and magnetic structure of $\alpha$-RuCl3
• The Flux-Phase of the Half-Filled Band
• 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
• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
• Robustness of a perturbed topological phase
• Large field-induced gap of Kitaev-Heisenberg paramagnons in $\alpha$-RuCl${}_3$
• Emergence of a Field-Driven U(1) Spin Liquid in the Kitaev Honeycomb Model
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Quantum spin liquid signatures in Kitaev-like frustrated magnets
• 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
• Self-duality and bound states of the toric code model in a transverse field
• Strong-weak coupling self-duality in the two-dimensional quantum phase transition of $p+ip$ superconducting arrays
• Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays
• Antiferromagnetic resonance and terahertz continuum in $\alpha -$RuCl${}_3$
• Resolving continua of fractional excitations by spinon echo in THz 2D coherent spectroscopy
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• The Density Matrix Renormalization Group for Strongly Correlated Electron Systems: A Generic Implementation
• Unconventional spin dynamics in the honeycomb-lattice material $\alpha$-RuCl${}_3$: high-field ESR studies
• Magnetic field induced intermediate quantum spin-liquid with a spinon Fermi surface
• Successive Majorana Topological Transitions Driven by a Magnetic Field in the Kitaev Model
• SU(2) Slave Fermion Solution of the Kitaev Honeycomb Lattice Model
• Theory of two-dimensional nonlinear spectroscopy for the Kitaev spin liquid
• Synthetic Topological Degeneracy by Anyon Condensation
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Dynamics of visons and thermal Hall effect in perturbed Kitaev models
• Intermediate gapless phase and topological phase transition of Kitaev model in a uniform magnetic field
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Theory of the Kitaev model in a [111] magnetic field
• Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling
• Signatures of magnetic-field-driven quantum phase transitions in the entanglement entropy and spin dynamics of the Kitaev honeycomb model
• Linear and Nonlinear Optical Responses in Kitaev Spin Liquids
• Floquet engineering of Mott insulators with strong spin-orbit coupling
• Tuning topological orders by a conical magnetic field in the Kitaev model
• Time Evolution with the DMRG Algorithm: A Generic Implementation for Strongly Correlated Electronic Systems
• Rigorous Calculations of Non-Abelian Statistics in the Kitaev Honeycomb Model
• Dynamical anyon generation in Kitaev honeycomb non-Abelian spin liquids
• Two-Magnon Bound States in the Kitaev Model in a $[111]$-Field
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Field stability of Majorana spin liquids in antiferromagnetic Kitaev models
• Phases and Quantum Phase Transitions in an Anisotropic Ferromagnetic Kitaev-Heisenberg-$\Gamma$ Magnet
• Gapless to gapless phase transitions in quantum spin chains
• Detection of long-range entanglement in gapped quantum spin liquids by local measurements

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• Dimensional reduction of Kitaev spin liquid at quantum criticality
• Machine learning reveals features of spinon Fermi surface
• Detection of anyon braiding through pump-probe spectroscopy
• Sub-symmetry Protected Topology in Topological Insulators and Superconductors
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Post-experiment coincidence detection techniques for direct detection of two-body correlations
• Tunable anyonic permeability across ${\mathbb{Z}}_2$ spin liquid junctions
• Hidden subsystem symmetry protected states in competing topological orders