Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet

Abstract

The spin-1/2 Heisenberg kagome antiferromagnet is one of the paradigmatic playgrounds for frustrated quantum magnetism, with an extensive number of competing resonating valence bond (RVB) states emerging at low energies, including gapped and gapless spin liquids and valence bond crystals. Here we revisit the crossover from this quantum RVB phase to a semiclassical regime brought about by anisotropic Kitaev interactions, and focus on the precise mechanisms underpinning this crossover. To this end, we introduce a simple parametrization of the classical ground states (GSs) in terms of emergent Ising-like variables, and use this parametrizaton: i) to construct an effective low-energy description of the order-by-disorder mechanism operating in a large part of the phase diagram, and ii) to contrast, side by side, exact diagonalization data obtained from the full basis with that obtained from the restricted (orthonormalized) basis of classical GSs. The results reveal that fluctuation corrections from states outside the restricted basis are strongly quenched inside the semiclassical regime (due to the large anisotropy spin gaps), and that the RVB phase survives up to a relatively large value of Kitaev anisotropy $K$. We further find that the pure Kitaev model admits a subextensive number of one-dimensional symmetries, which explains naturally the absence of classical and quantum order by disorder reported previously.

arXiv comment16 pages, 14 figures

References in corpus (65)

• 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
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• 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
• Kitaev quantum spin liquid - concept and materialization
• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• Models and Materials for Generalized Kitaev Magnetism
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{é} lattice: an approach through exact spectra analysis
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Hunting Majorana Fermions in Kitaev Magnets
• Low-energy sector of the S=1/2 Kagome antiferromagnet
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Protected Qubits and Chern Simons theories in Josephson Junction Arrays
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• The Quantum Compass Model on the Square Lattice
• Theory of the field-revealed Kitaev spin liquid
• Generalized Elitzur's Theorem and Dimensional Reduction
• RVB description of the low-energy singlets of the spin 1/2 kagome antiferromagnet
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Heisenberg-Kitaev physics in magnetic fields
• Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice
• Low energy excitations of the kagome antiferromagnet and the spin gap issue
• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet
• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets
• Z_2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model
• Removing the spin ice cap: magnetic ground states of rare earth tripod kagome lattice Mg${}_2$RE${}_3$Sb${}_3$O${}_{14}$ (RE = Gd, Dy, Er)
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Emergent Order in the Kagome Ising Magnet Dy3Mg2Sb3O14
• Classical spin liquid instability driven by off-diagonal exchange in strong spin-orbit magnets
• Effective Quantum Dimer Model for the Kagome Heisenberg Antiferromagnet: Nearby Quantum Critical Point and Hidden Degeneracy
• Kitaev materials beyond iridates: order by quantum disorder and Weyl magnons in rare-earth double perovskites
• Scalar Chiral Spin-1/2 Order on Kagome Lattices in Nd3Sb3Mg2O14
• Quantum dimer model with extensive ground-state entropy on the kagome lattice
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Magnetic Orders Proximal to the Kitaev Limit in Frustrated Triangular Systems: Application to Ba${}_3$IrTi${}_2$O${}_9$
• Magnetic Field Induced Competing Phases in Spin-Orbital Entangled Kitaev Magnets
• Structural and magnetic properties of two branches of the Tripod Kagome Lattice family A${}_2$RE${}_3$Sb${}_3$O${}_{14}$ (A = Mg, Zn; RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb)
• Quantum order by disorder in the Kitaev model on a triangular lattice
• Magnetic structure and excitation spectrum of the hyperhoneycomb Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Kitaev-Heisenberg model in a magnetic field: order-by-disorder and commensurate-incommensurate transitions
• Quantum spin liquid in the semiclassical regime
• Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods
• Magnetic field-induced evolution of intertwined orders in the Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet
• Quantum dimer model for the spin-1/2 kagome Z2 spin liquid
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Ground-state phase diagram of the Kitaev-Heisenberg model on a kagome lattice
• Ground state phase diagram of Kitaev-Heisenberg model on honeycomb-triangular lattice
• Collective spin dynamics of Z2 vortex crystals in triangular Kitaev-Heisenberg antiferromagnets
• Magnetization plateau and supersolid phases in the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice
• Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$

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• The nature of low-temperature spin-freezing in frustrated Kitaev magnets