Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation

Abstract

Motivated by the recent synthesis of two insulating Li${}_2$IrO${}_3$ polymorphs, where Ir${}^{4+}$ $S_{eff}$=1/2 moments form 3D ("harmonic") honeycomb structures with threefold coordination, we study magnetic Hamiltonians on the resulting $\beta$-Li${}_2$IrO${}_3$ hyperhoneycomb lattice and $\gamma$-Li${}_2$IrO${}_3$ stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities suggest that Kitaev interactions, predicted for the ideal 90${}^{\circ }$ Ir-O-Ir bonds, are sizable in these materials. We first consider pure Kitaev interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL) with emergent Majorana fermions and Z${}_2$ flux loops. Unlike 2D QSLs, the 3D QSL is stable to finite temperature, with $T_c\approx |K|/100$. On including Heisenberg couplings, exact solubility is lost. However, by noting that the shortest closed loop $\ell$ is relatively large in these structures, we construct an $\ell \to \infty$ approximation by defining the model on the Bethe lattice. The phase diagram of the Kitaev-Heisenberg model on this lattice is obtained directly in the thermodynamic limit, using tensor network states and the infinite-system time-evolving-block-decimation (iTEBD) algorithm. Both magnetically ordered and gapped QSL phases are found, the latter being identified by an entanglement fingerprint.

v2: added results on a new 3D lattice, the n=1 harmonic honeycomb (also known as the stripyhoneycomb lattice), identified in recent experiments on Li2IrO3 (1402.3254). Comparison to magnetic properties measured in 1402.3254 are also added. v3: published version. Main text 16 pages, 12 figures; appendix 6 pages, 6 figures

References in corpus (32)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Identifying Topological Order by Entanglement Entropy
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• A new spin-anisotropic harmonic honeycomb iridate
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Crystal field splitting and correlation effect on the electronic structure of A2IrO3
• Na2IrO3 as a spin-orbit-assisted antiferromagnetic insulator with a 340 meV gap
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Spin-orbit effects in Na${}_4$Ir${}_3$O${}_8$, a hyper-kagomé lattice antiferromagnet
• Gapless spin liquids on the three dimensional hyper-kagome lattice of Na${}_4$Ir${}_3$O${}_8$
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8
• Heisenberg-Kitaev model on hyperhoneycomb lattice
• Na4Ir3O8 as a 3D spin liquid with fermionic spinons
• Efficient simulation of infinite tree tensor network states on the Bethe lattice
• Magnetic ordering phenomena of interacting quantum spin Hall models
• The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
• Evolution of Magnetism in Single-Crystal Honeycomb Iridates
• Variational study of J1-J2 Heisenberg model on Kagome lattice using projected Schwinger boson wave functions
• Effect of nonmagnetic dilution in honeycomb lattice iridates Na${}_2$IrO${}_3$ and Li${}_2$IrO${}_3$
• Effect of isoelectronic doping on honeycomb lattice iridate A_2IrO_3
• Electronic excitations in the edge-shared relativistic Mott insulator: Na${}_2$IrO${}_3$
• Order-by-disorder and magnetic field response in Heisenberg-Kitaev model on a hyperhoneycomb lattice
• Hole propagation in the Kitaev-Heisenberg model: From quasiparticles in quantum Neel states to non-Fermi liquid in the Kitaev phase
• Featureless quantum spin liquid, 1/3-magnetization plateau state and exotic thermodynamic properties of spin-1/2 frustrated Heisenberg antiferromagnet on an infinite Husimi lattice

Cited by in corpus (99)

• Quantum entanglement in condensed matter systems
• 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
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• A new spin-anisotropic harmonic honeycomb iridate
• Hunting Majorana Fermions in Kitaev Magnets
• Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Symmetry Demanded Topological Nodal-line Materials
• The Challenge of Spin-Orbit-Tuned Ground States in Iridates
• Recent progress on correlated electron systems with strong spin-orbit coupling
• Dynamics of Fractionalization in Quantum Spin Liquids
• Classification of gapless Z2 spin liquids in three-dimensional Kitaev models
• Relation between Kitaev magnetism and structure in $\alpha$-RuCl${}_3$
• Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
• Heisenberg-Kitaev physics in magnetic fields
• Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates $\beta$- and $\gamma$-Li${}_2$IrO${}_3$
• Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice
• Weyl spin liquids
• Honeycomb Layered Oxides: Structure, Energy Storage, Transport, Topology and Relevant Insights
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Classical spin liquid instability driven by off-diagonal exchange in strong spin-orbit magnets
• Quantum Magnetism in Minerals
• Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3
• Thermodynamic Evidence of Proximity to a Kitaev Spin-Liquid in Ag${}_3$LiIr${}_2$O${}_6$
• Breakdown of magnetic order in the pressurized Kitaev iridate $\beta$-Li${}_2$IrO${}_3$
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Path to stable quantum spin liquids in spin-orbit coupled correlated materials
• Loop-nodal and Point-nodal Semimetals in Three-dimensional Honeycomb Lattices
• Theory of Raman response in three-dimensional Kitaev spin liquids: application to $\beta -$ and $\gamma -$Li${}_2$IrO${}_3$ compounds
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Pressure-tuning of bond-directional exchange interactions and magnetic frustration in hyperhoneycomb iridate $\beta$-$\mathrm{L}{\mathrm{i}}_2\mathrm{Ir}{\mathrm{O}}_3$
• Topological spinon semimetals and gapless boundary states in three dimensions
• Scale-invariant magnetic anisotropy in RuCl${}_3$ at high magnetic fields
• Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces
• Magnetic structure and excitation spectrum of the hyperhoneycomb Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• The vicinity of hyper-honeycomb $\beta$-Li2IrO3 to a three-dimensional Kitaev spin liquid state
• A universal tensor network algorithm for any infinite lattice
• Revisiting the Kitaev material candidacy of Ir4+ double perovskite iridates
• Crystalline Kitaev spin liquids
• New Honeycomb Iridium (V) Oxides: NaIrO${}_3$ and Sr${}_3$CaIr${}_2$O${}_9$
• Predominance of the Kitaev interaction in a three-dimensional honeycomb iridate: from ab-initio to spin model
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Magnetic field-induced evolution of intertwined orders in the Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Revealing frustrated local moment model for pressurized hyperhoneycomb iridate: paving a way toward quantum spin liquid
• Functional renormalization group study of the Kitaev-$\Gamma$ model on the honeycomb lattice and emergent incommensurate magnetic correlations
• Symmetry Enrichment in Three-Dimensional Topological Phases
• Resonant Raman scattering theory for Kitaev models and their Majorana fermion boundary modes
• Magnetic field-dependent low-energy magnon dynamics in $\alpha$-RuCl3
• Quantum and classical behavior of spin-$S$ Kitaev models in an anisotropic limit
• Neutron scattering signatures of the 3D hyper-honeycomb Kitaev quantum spin-liquid
• Structural, electronic, and magnetic properties of nearly-ideal $J_{\mathrm{eff}}$ $=$ 1/2 iridium halides
• Pressure-induced structural dimerization in the hyperhoneycomb iridate $\beta$-Li${}_2$IrO${}_3$ at low temperatures
• Stacking faults in $\alpha$-RuCl${}_3$ revealed by local electric polarization
• Majorana spectroscopy of 3D Kitaev spin-liquids
• Finite-temperature phase transition to a Kitaev spin liquid phase on a hyperoctagon lattice: A large-scale quantum Monte Carlo study
• Uniaxial and hydrostatic pressure effects in alpha-RuCl3 single crystals via thermal-expansion measurements
• Chiral spin-order in some purported Kitaev spin-liquid compounds
• Magnetic three states of matter: A quantum Monte Carlo study of spin liquids
• Counter-rotating spiral order in three dimensional iridates: signature of hidden symmetry in Kitaev-$\Gamma$ model
• Vacancies in the Kitaev quantum spin liquids on the 3D hyper-honeycomb lattice
• Generic Field-Driven Phenomena in Kitaev Spin Liquids: Canted Magnetism and Proximate Spin Liquid Physics
• $\mathrm{SU}(4)$-Symmetric Quantum Spin-Orbital Liquids on Various Lattices
• Photoexcited states of the harmonic honeycomb iridate γ-Li${}_2$IrO${}_3$
• Magnetism on the stretched diamond lattice in lanthanide orthotantalates
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Field stability of Majorana spin liquids in antiferromagnetic Kitaev models
• Raman scattering in correlated thin films as a probe of chargeless surface states
• Electronic excitations in $\gamma$-Li${}_2$IrO${}_3$
• Weyl and nodal ring magnons in three-dimensional honeycomb lattices
• Classification and properties of quantum spin liquids on the hyperhoneycomb lattice
• Spin dynamics of counterrotating Kitaev spirals via duality
• Resonant inelastic x-ray scattering spectra in the hyperhoneycomb iridate $\beta$-Li${}_2$IrO${}_3$: First principles calculations
• Heisenberg-Kitaev Models on Hyperhoneycomb and Stripyhoneycomb Lattices: 3D-2D Equivalence of Ordered States and Phase Diagrams
• Evolution of Magnetism in the $N{a}_{3-d}N{a}_{1-x}M{g}_{x}I{r}_2{O}_6$ Series of Honeycomb Iridates
• Chiral spin liquids with crystalline ${\mathbb{Z}}_2$ gauge order in a three-dimensional Kitaev model
• Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$
• Hidden spin-orbital order in the Kitaev hyperhoneycomb $\beta$-Li${}_2$IrO${}_3$
• Symmetry-protected topological magnons in three dimensional Kitaev materials
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Topological entanglement entropy of three-dimensional Kitaev model
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Projective symmetry of partons in Kitaev's honeycomb model
• Vibronic effect on resonant inelastic x-ray scattering in cubic iridium hexahalides
• A theory of the quantum spin liquid in the hyper-honeycomb metal-organic framework [(C${}_2$H${}_5$)${}_3$NH]${}_2$Cu${}_2$(C${}_2$O${}_4$)${}_3$ from first principles
• From chiral d-wave to nodal line superconductivity in the harmonic honeycomb lattices
• Projective-symmetry-group analysis of inelastic light scattering in Kitaev spin balls
• Anion-Anion Bonding and the Topology in Ternary Iridium Seleno-Stannides
• Kitaev model in regular hyperbolic tilings
• Robust semi-Dirac points and unconventional topological phase transitions in doped superconducting Sr2IrO4 tunnel coupled to t2g electron systems
• Correlations generated from high-temperature states: nonequilibrium dynamics in the Fermi-Hubbard model
• Barrier tunneling of the Loop-Nodal Semimetal in the Hyperhoneycomb lattice
• Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
• Spin correlation and Majorana spectrum in chiral spin liquids in a decorated-honeycomb Kitaev model
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties
• Spin-$1$ $J_1-J_2-J_3$ ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice: A bosonic approach
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Global constraints on $Z_2$ fluxes in two different anisotropic limits of a hypernonagon Kitaev model
• Three-dimensional spin-orbital liquids