An investigation of the quantum $J_1-J_2-J_3$ model on the honeycomb lattice

Abstract

We have investigated the quantum $J_1-J_2-J_3$ model on the honeycomb lattice with exact diagonalizations and linear spin-wave calculations for selected values of $J_2/J_1$, $J_3/J_1$ and antiferromagnetic ($J_1>0$) or ferromagnetic ($J_1<0$) nearest neighbor interactions. We found a variety of quantum effects: "order by disorder" selection of a N{é}el ordered ground-state, good candidates for non-classical ground-states with dimer long range order or spin-liquid like. The purely antiferromagnetic Heisenberg model is confirmed to be N{é}el ordered. Comparing these results with those observed on the square and triangular lattices, we enumerate some conjectures on the nature of the quantum phases in the isotropic models.

14 pages, 22 Postscript figures, uses svjour.cls and svepj.clo, submitted to European Physical Journal B: condensed matter physic

Cited by in corpus (176)

• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Models and Materials for Generalized Kitaev Magnetism
• Suppression of magnetic ordering in XXZ-type antiferromagnetic monolayer NiPS3
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Band geometry, Berry curvature and superfluid weight
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice
• Kitaev-Heisenberg-J2-J3 model for the iridates A2IrO3
• Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $\alpha$-RuCl${}_3$ and Na${}_2$IrO${}_3$
• Lattice symmetries and regular states in classical frustrated antiferromagnets
• The phase diagram of the hexagonal lattice quantum dimer model
• Kitaev interactions in the Co honeycomb antiferromagnets Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Magnetic properties of the honeycomb oxide Na${}_2$Co${}_2$TeO${}_6$
• Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model
• Nature of the spin liquid state of the Hubbard model on honeycomb lattice
• Zigzag antiferromagnetic ground state with anisotropic correlation lengths in the quasi-2D honeycomb lattice compound Na2Co2TeO6
• The magnetic properties and structure of the quasi-two-dimensional antiferromagnet CoPS${}_3$
• The magnetic exchange parameters and anisotropy of the quasi-two dimensional antiferromagnet NiPS${}_3$
• Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
• Magnetic order and paramagnetic phases in the quantum J1-J2-J3 honeycomb model
• Heisenberg-Kitaev physics in magnetic fields
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Deconfined criticality in the frustrated Heisenberg honeycomb antiferromagnet
• Low energy excitations of the kagome antiferromagnet and the spin gap issue
• Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: the $J_1$--$J_2$--$J_3$ model
• Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet
• Ground states of quantum antiferromagnets in two dimensions
• beta-Cu2V2O7: a spin-1/2 honeycomb lattice system
• Z_2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model
• Quantum disordered phase on the frustrated honeycomb lattice
• Emergent $\mathrm{SU}(4)$ Symmetry in $\alpha$-ZrCl${}_3$ and Crystalline Spin-Orbital Liquids
• Frustrated quantum magnets
• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory
• Phase Diagram of the J1, J2, J3 Heisenberg Models on the Honeycomb Lattice: A Series Expansion Study
• Geometrical frustration versus Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$
• Quantum paramagnetic ground states on the honeycomb lattice and field-induced transition to Néel order
• Quantum paramagnets on the honeycomb lattice and field-induced Néel order: Possible application to Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$)
• Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice
• Excitations in the ordered and paramagnetic states of honeycomb magnet Na2Co2TeO6
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• XY magnetism, Kitaev exchange, and long-range frustration in the $J_{\mathrm{eff}}=1/2$ honeycomb cobaltates
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• Numerical treatment of spin systems with unrestricted spin length $S$: A functional renormalization group study
• Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: $J_1$--$J_2$ model
• Magnetic Couplings in Edge-Sharing High-Spin $d^7$ Compounds
• Correlated Dirac Particles and Superconductivity on the Honeycomb Lattice
• Antiferromagnetism at T > 500 K in the Layered Hexagonal Ruthenate SrRu2O6
• Spin-waves in 2D honeycomb lattice $XXZ$-type van der Waals antiferromagnet CoPS${}_3$
• Spin-gap phase of a quantum spin system on a honeycomb lattice
• Short range order in the quantum XXZ honeycomb lattice material BaCo${}_2$(PO${}_4$)${}_2$
• Ab initio guided minimal model for the "Kitaev" material BaCo${}_2$(AsO${}_4$)${}_2$: Importance of direct hopping, third-neighbor exchange and quantum fluctuations
• Topological magnon bands in the zigzag and stripy phases of antiferromagnetic honeycomb lattice
• Frustrated magnetism and resonating valence bond physics in two-dimensional kagome-like magnets
• Stability of the spiral spin liquid in MnSc${}_2$S${}_4$
• Detecting spontaneous symmetry breaking in finite-size spectra of frustrated quantum antiferromagnets
• Competition between spin liquids and valence-bond order in the frustrated spin-$1/2$ Heisenberg model on the honeycomb lattice
• Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice
• Randomness-induced quantum spin liquid behavior in the s=1/2 random J1-J2 Heisenberg antiferromagnet on the honeycomb lattice
• Excitation band topology and edge matter waves in Bose-Einstein condensates in optical lattices
• Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizations
• Quantum phase diagram of the spin-$1$ $J_1-J_2$ Heisenberg model on the honeycomb lattice
• Magnetism in spin models for depleted honeycomb-lattice iridates: Spin-glass order towards percolation
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Quantum Phase Transitions around the Staggered Valence Bond Solid
• 1-Dimensional behavior and sliding Luttinger liquid phase in a frustrated spin-1/2 crossed chain model: contribution of exact diagonalizations
• Unusual magnetic phases in the strong interaction limit of two-dimensional topological band insulators in transition metal oxides
• Observation of a 1/3 Magnetisation Plateau Phase as Evidence for the Kitaev Interaction in a Honeycomb-Lattice Antiferromagnet
• Structural Transition of Li2RuO3 Induced by Molecular-Orbit Formation
• Degenerate manifolds, helimagnets, and multi-$\mathbf{Q}$ chiral phases in the classical Heisenberg antiferromagnet on the face-centered-cubic lattice
• Role of quantum fluctuations on spin liquids and ordered phases in the Heisenberg model on the honeycomb lattice
• Ground state properties, excitation spectra and phase transitions in the $S=1/2$ and $S=3/2$ bilayer Heisenberg models on the honeycomb Lattice
• Low-temperature magnetic ordering and structural distortions in Vanadium Sesquioxide (V${}_2$O${}_3$)
• Classical spin-liquid on the maximally frustrated honeycomb lattice
• Anisotropy governed competition of magnetic phases in the honeycomb quantum magnet Na${}_3$Ni${}_2$SbO${}_6$ studied by dilatometry and high-frequency ESR
• Frustrated Heisenberg antiferromagnet on the honeycomb lattice: Spin gap and low-energy parameters
• Static and Dynamic Magnetic Response of Fragmented Haldane-like Spin Chains in Layered Li3Cu2SbO6
• Quantum paramagnetism and magnetization plateaus in a kagome-honeycomb Heisenberg antiferromagnet
• Quantum phases in the frustrated Heisenberg model on the bilayer honeycomb lattice
• Finite size effects and magnetic order in the spin-1/2 honeycomb lattice compound InCu{2/3}V{1/3}O{3}
• Magnetism of the 2D honeycomb layered Na2Ni2TeO6 compound driven by intermediate Na-layer crystal-structure
• Ground-state phases of the frustrated spin-1/2 $J_1$--$J_2$--$J_3$ Heisenberg ferromagnet ($J_1<0$) on the honeycomb lattice with $J_3=J_2>0$
• Signature of a randomness-driven spin-liquid state in a frustrated magnet
• Theory of Ca${}_{10}$Cr${}_7$O${}_{28}$ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics
• Emergent Potts order in the kagomé $J_1-J_3$ Heisenberg model
• The frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ isotropic $XY$ model on the honeycomb lattice
• How many spin liquids are there in Ca${}_{10}$Cr${}_7$O${}_{28}$?
• Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice
• Spiral antiferromagnets beyond the spin-wave approximation: frustrated $XY$ and Heisenberg models in the honeycomb lattice
• Complete phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ model (with $J_3=J_2$) on the honeycomb lattice
• Low energy structure of spiral spin liquids
• Plaquette-RVB state in the Frustrated Honeycomb Antiferromagnet
• Anisotropic RKKY interaction in spin polarized graphene
• Phase diagram of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ $XXZ$ model on the honeycomb lattice
• Extended degeneracy and order by disorder in the square lattice J${}_1$-J${}_2$-J${}_3$ model
• Quantum Phases in the Honeycomb-Lattice $J_1$--$J_3$ Ferro-Antiferromagnetic Model
• Easy-plane anisotropic-exchange magnets on a honeycomb lattice: quantum effects and dealing with them
• A frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model
• Ground-state phases of the spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet on the honeycomb lattice
• Nanoscale self-organisation and metastable non-thermal metallicity in Mott insulators
• Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets
• Quantum phases and phase transitions of Mott insulators
• Spin wave spectra of single crystal CoPS${}_3$
• Proximate Dirac spin liquid in honeycomb lattice $J_1$-$J_3$ XXZ model: Numerical study and application to cobaltates
• Magnetism and superconductivity in the layered hexagonal transition metal pnictides
• Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model
• Dynamical properties of Néel and valence-bond phases in the $J_1-J_2$ model on the honeycomb lattice
• Anisotropic Quantum Spin Hall Effect, Spin-Orbital Textures and Mott Transition
• Anomalous Spin Dynamics observed by High Frequency ESR in Honeycomb Lattice Antiferromagnet InCu2/3V1/3O3
• Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
• Thermal Hall responses in frustrated honeycomb spin systems
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Dimensionality dependent electronic structure of the exfoliated van der Waals antiferromagnet NiPS${}_3$
• Evidence of a spin liquid phase in the frustrated honeycomb lattice
• Semiclassical theory for liquid-like behaviour of the frustrated magnet ${\mathrm{Ca}}_{10}{\mathrm{Cr}}_7{\mathrm{O}}_{28}$
• Spin Dynamics in a Stripe-ordered Buckled Honeycomb Lattice Antiferromagnet Ba${}_2$NiTeO${}_6$
• Temperature-Induced Magnonic Chern Insulator in Collinear Antiferromagnets
• First-order transitions at the Neel temperatures of trigonal SrMn2P2 and CaMn2P2 single crystals containing corrugated-honeycomb Mn sublattices
• Affine lattice construction of spiral surfaces in classical Heisenberg models
• Suppression of Antiferromagnetic Order by Strain in Honeycomb Cobaltate: Implication for Quantum Spin Liquid
• High-angular momentum excitations in collinear antiferromagnet FePS${}_3$
• A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer
• Exotic magnetic field-induced spin-superstructures in a mixed honeycomb triangular lattice system
• Ferrimagnetism from triple-q order in Na${}_2$Co${}_2$TeO${}_6$
• Anisotropic frustrated Heisenberg model on the honeycomb lattice
• Robust intralayer antiferromagnetism and tricriticality in a van der Waals compound: VBr3 case
• Honeycomb antiferromagnet with a triply degenerate dimer ground state
• Spin Waves and Dirac Magnons in a Honeycomb Lattice Zig-zag Antiferromagnet BaNi2(AsO4)2
• Spin dynamics and continuum spectra of the honeycomb J1-J2 antiferromagnetic Heisenberg model
• Entanglement and quantum correlations in the XX spin-$1/2$ honeycomb lattice
• Frustrated Magnetic Cycloidal Structure and Emergent Potts Nematicity in CaMn${}_2$P${}_2$
• {23}Na nuclear spin-lattice relaxation studies of Na2Ni2TeO6
• Field theories of paramagnetic Mott insulators
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Self consistent study of the quantum phases in a frustrated antiferromagnet on the bilayer honeycomb lattice
• Frustrated Heisenberg antiferromagnet on the honeycomb lattice with spin quantum number $s\ge 1$
• Magnetism and field-induced effects in the S = 5/2 honeycomb lattice antiferromagnet FeP3SiO11
• The magnetic order of a manganese vanadate system with two-dimensional striped triangular lattice
• Hydrostatic pressure effect on Co-based honeycomb magnet BaCo2(AsO4)2
• The decisive role of magnetic anisotropy in honeycomb layered Li${}_3$Ni${}_2$SbO${}_6$ and Na${}_3$Ni${}_2$SbO${}_6$
• Quantum phase diagram of $J_1-J_2$ Heisenberg $S=1/2$ antiferromagnet in honeycomb lattice: a modified spin wave study
• Longitudinal Magnetization and specific heat of the anisotropic Heisenberg antiferromagnet on Honeycomb lattice
• Study of the bilinear biquadratic Heisenberg model on a honeycomb lattice via Schwinger bosons
• Antiferromagnetic order without recourse to staggered fields
• Electrically tunable room-temperature ferromagnetism in CrBr${}_3$
• Disorder effects in spiral spin liquids: Long-range spin textures, Friedel-like oscillations, and spiral spin glasses
• Exotic topological point and line nodes in the plaquette excitations of a frustrated Heisenberg antiferromagnet on the honeycomb lattice
• Collinear antiferromagnetic phases of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg model on an $AA$-stacked bilayer honeycomb lattice
• Spin-orbit entangled moments and magnetic exchange interactions in cobalt-based honeycomb magnets BaCo${}_2$($X$O${}_4$)${}_2$ ($X$ = P, As, Sb)
• Classical and quantum spin liquids
• From Frustrated to Unfrustrated: Coupling two triangular-lattice itinerant Quantum Magnets
• Néel Ordering in the Distorted Honeycomb Pyrosilicate: C-Er${}_2$Si${}_2$O${}_7$
• Zero Temperature Phase Diagram of the Classical Kane-Mele-Heisenberg Model
• ${\mathbb{Z}}_2$ vortices in the ground states of classical Kitaev-Heisenberg models
• Optimizing configurations for determining the magnetic model based on ab-initio calculations
• Low-energy parameters and spin gap of a frustrated spin-$s$ Heisenberg antiferromagnet with $s\le \frac{3}{2}$ on the honeycomb lattice
• Field-Induced Magnon Decay, Magnon Shadows, and Roton-like Excitations in the Honeycomb Antiferromagnet YbBr${}_3$
• 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
• Dualities between 2+1d fusion surface models from braided fusion categories
• Transverse Magnetic Susceptibility of a Frustrated Spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg Antiferromagnet on a Bilayer Honeycomb Lattice
• Valence Bond Phases in $S=1/2$ Kane-Mele-Heisenberg Model
• Understanding the magnetic interactions of the zig-zag honeycomb lattice: Application to $\alpha$-RuCl${}_3$
• Demystifying quantum escapism on the honeycomb lattice
• Quantum disordered ground state for the frustrated square lattice
• Incommensurate and commensurate antiferromagnetic states in CaMn2As2 and SrMn2As2 revealed by 75As NMR
• Finite-Size Spectral Signatures of Order by Quantum Disorder: A Perspective from Anderson's Tower of States
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Stabilization of zigzag order in NiPS${}_3$ via positive biquadratic interaction
• Magnetic anisotropy and magnetic ordering of transition-metal phosphorus trisulfides
• Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi }$ model in honeycomb lattice: thermal Hall signature