Classical and quantum spin dynamics of the honeycomb $\Gamma$ model

Abstract

Quantum to classical crossover is a fundamental question in dynamics of quantum many-body systems. In frustrated magnets, for example, it is highly non-trivial to describe the crossover from the classical spin liquid with a macroscopically-degenerate ground-state manifold, to the quantum spin liquid phase with fractionalized excitations. This is an important issue as we often encounter the demand for a sharp distinction between the classical and quantum spin liquid behaviors in real materials. Here we take the example of the classical spin liquid in a frustrated magnet with novel bond-dependent interactions to investigate the classical dynamics, and critically compare it with quantum dynamics in the same system. In particular, we focus on signatures in the dynamical spin structure factor. Combining Landau-Lifshitz dynamics simulations and the analytical Martin-Siggia-Rose (MSR) approach, we show that the low energy spectra are described by relaxational dynamics and highly constrained by the zero mode structure of the underlying degenerate classical manifold. Further, the higher energy spectra can be explained by precessional dynamics. Surprisingly, many of these features can also be seen in the dynamical structure factor in the quantum model studied by finite-temperature exact diagonalization. We discuss the implications of these results, and their connection to recent experiments on frustrated magnets with strong spin-orbit coupling.

18 pages, 19 figures

References in corpus (36)

• 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
• Correlated quantum phenomena in the strong spin-orbit regime
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Models and Materials for Generalized Kitaev Magnetism
• 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
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes
• Breakdown of Magnons in a Strongly Spin-Orbital Coupled Magnet
• 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
• Canonical Thermal Pure Quantum State
• Thermal Pure Quantum States at Finite Temperature
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Large field-induced gap of Kitaev-Heisenberg paramagnons in $\alpha$-RuCl${}_3$
• Field-induced quantum criticality in the Kitaev system $\alpha$-RuCl${}_3$
• Dynamics of Fractionalization in Quantum Spin Liquids
• Probing $\alpha$-RuCl${}_3$ Beyond Magnetic Order: Effects of Temperature and Magnetic Field
• Quantum spin liquid signatures in Kitaev-like frustrated magnets
• Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na${}_2$IrO${}_3$
• Kitaev Materials
• Quantum Lattice Model Solver $\mathcal{H}\Phi$
• Classical spin liquid instability driven by off-diagonal exchange in strong spin-orbit magnets
• Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets
• Path to stable quantum spin liquids in spin-orbit coupled correlated materials
• Comprehensive study of the dynamics of a classical Kitaev spin liquid
• Stochastic Estimation of Nuclear Level Density in the Nuclear Shell Model: An Application to Parity-Dependent Level Density in ${}^{58}$Ni
• Numerical Algorithm for Exact Finite Temperature Spectra and Its Application to Frustrated Quantum Spin Systems
• Incarnation of Majorana Fermions in Kitaev Quantum Spin Lattice
• Transverse thermoelectric transport in a model of many competing order parameters

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• Thermodynamic evidence of fractionalized excitations in α-RuCl3
• Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Giant magnetic in-plane anisotropy and competing instabilities in Na3Co2SbO6
• Variational study of the Kitaev-Heisenberg-Gamma model
• Emergence of a nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets
• Classical spin dynamics based on SU($N$) coherent states
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice
• Gapless quantum spin liquid in a honeycomb $\Gamma$ magnet
• THz excitations in α-RuCl3: Majorana fermions, rigid-plane shear and compression modes
• Vison-Majorana complex zero-energy resonance in Kitaev's spin liquid
• Plaquette order in classical spin liquid stabilized by strong off-diagonal exchange
• Thermal spin dynamics of Kitaev magnets $-$ scattering continua and magnetic field induced phases within a stochastic semiclassical approach
• Extent of frustration in the classical Kitaev-$\Gamma$ model via bond anisotropy
• Update of $\mathcal{H}\Phi$: Newly added functions and methods in versions 2 and 3
• Ground-state properties of the $K-\Gamma$ model on a honeycomb lattice
• Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice
• Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets
• Confinement transition in a Kitaev-like honeycomb model with bond anisotropy
• Magnetism and field-induced effects in the S = 5/2 honeycomb lattice antiferromagnet FeP3SiO11
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Disentangling spin excitation continua in classical and quantum magnets using 2D nonlinear spectroscopy
• Dynamical precession of spin in the two-dimensional spin-orbit coupled systems
• A High-Performance Implementation of Atomistic Spin Dynamics Simulations on x86 CPUs
• Classical spin models of the windmill lattice and their relevance for PbCuTe${}_2$O${}_6$
• High-fidelity dimer excitations using quantum hardware
• Temperature dependence of the $(\pi ,0)$ anomaly in the excitation spectrum of the 2D quantum Heisenberg antiferromagnet
• Static and dynamical magnetic properties of the extended Kitaev-Heisenberg model with spin vacancies
• Complex orders and chirality in the classical Kitaev-$\Gamma$ model
• Emulation of quantum correlations by classical dynamics in a spin-1/2 Heisenberg chain
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Pulsed Neutron Spectroscopy of Low Dimensional Magnets: Past, Present, and Future
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3
• Honeycomb-lattice Gamma model in a magnetic field: hidden Néel order and spin-flop transition