Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method

Abstract

We study the spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice for $S=1/2$, $1$ and $3/2$, by using the coupled cluster method (CCM) of microscopic quantum many-body theory. This system is one of the earliest extensions of the Kitaev model and is believed to contain two extended spin liquid phases for any value of the spin quantum number $S$. We show that the CCM delivers accurate estimates for the phase boundaries of these spin liquid phases, as well as other transition points in the phase diagram. Moreover, we find evidence of two unexpected narrow phases for $S=1/2$, one sandwiched between the zigzag and ferromagnetic phases and the other between the Néel and the stripy phases. The results establish the CCM as a versatile numerical technique that can capture the strong quantum-mechanical fluctuations that are inherently present in generalized Kitaev models with competing bond-dependent anisotropies.

16 pages, 10 figures. This version: figures 5,8 and 10 updated, Table I updated, references added

References in corpus (36)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Models and Materials for Generalized Kitaev Magnetism
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2
• Microscopic mechanism for higher-spin Kitaev model
• Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3
• Theory of the field-revealed Kitaev spin liquid
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model
• Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids
• Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$\Gamma$ model on a honeycomb lattice
• Density-Matrix Renormalization Group Study of Extended Kitaev-Heisenberg Model
• Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions
• Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings
• 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
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Determining Kitaev interaction in spin-$S$ honeycomb Mott insulators
• Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB$m$ Approximation Scheme for Lattice Models
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Insights into the Anisotropic Spin-$S$ Kitaev Chain
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model

Cited by in corpus (6)

• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3
• Even-odd effect in multilayer Kitaev honeycomb magnets