Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice

Abstract

The Kitaev model, which hosts a quantum spin liquid (QSL) in the ground state, was originally defined on a two-dimensional honeycomb lattice, but can be straightforwardly extended to any tricoordinate lattices in any spatial dimensions. In particular, the three-dimensional (3D) extensions are of interest as a realization of 3D QSLs, and some materials like $\beta$-Li${}_2$IrO${}_3$, $\gamma$-Li${}_2$IrO${}_3$, and $\beta$-ZnIrO${}_3$ were proposed for the candidates. However, the phase diagrams of the models for those candidates have not been fully elucidated, mainly due to the limitation of numerical methods for 3D frustrated quantum spin systems. Here we study the Kitaev-Heisenberg model defined on a 3D hyperhoneycomb lattice, by using the pseudofermion functional renormalization group method. We show that the ground-state phase diagram contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases, similar to the two-dimensional honeycomb case. Our results respect the four-sublattice symmetry inherent in the model, which was violated in the previous study. Moreover, we also show how the phase diagram changes with the anisotropy in the interactions. The results provide a reference for the search of the hyperhoneycomb Kitaev materials.

8 pages, 6 figures

References in corpus (45)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Models and Materials for Generalized Kitaev Magnetism
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
• 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
• Vaporization of Kitaev spin liquids
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Quantum spin liquids in frustrated spin-1 diamond antiferromagnets
• Spiral order in the honeycomb iridate Li2IrO3
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3
• Electronic Structure of the Kitaev Material $\alpha$-${\text{RuCl}}_3$ Probed by Photoemission and Inverse Photoemission Spectroscopies
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Magnetic ordering phenomena of interacting quantum spin Hall models
• 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
• Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: A pseudo-fermion functional renormalization group perspective
• Spin-orbital entangled state and realization of Kitaev physics in 3d cobalt compounds: a progress report
• Functional-renormalization-group analysis of Dzyaloshinsky-Moriya and Heisenberg spin interactions on the kagome lattice
• Magnetic field induced quantum spin liquid in the two coupled trillium lattices of K${}_2$Ni${}_2$(SO${}_4$)${}_3$
• Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Temperature evolution of spin dynamics in two- and three-dimensional Kitaev models: Influence of fluctuating gauge fluxes
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice
• Critical scales in anisotropic spin systems from functional renormalization
• High temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high temperature series expansion study
• Electronic and magnetic properties of iridium ilmenites $A$IrO${}_3$ ($A=$ Mg, Zn, and Mn)
• Quantum Monte Carlo Simulation of Generalized Kitaev Models
• Magnon-spinon dichotomy in the Kitaev hyperhoneycomb $\beta$-Li${}_2$IrO${}_3$
• Enhanced symmetry-breaking tendencies in the $S=1$ pyrochlore antiferromagnet
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Magnetic Excitations and Interactions in the Kitaev Hyperhoneycomb Iridate $\beta$-Li${}_2$IrO${}_3$
• Feasibility of Kitaev quantum spin liquids in ultracold polar molecules
• Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$
• Quantum paramagnetism in the hyperhoneycomb Kitaev magnet $\beta$-ZnIrO${}_3$
• Moments and multiplets in moiré materials: A pseudo-fermion functional renormalization group for spin-valley models

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