SU(4) Theory for Spin Systems with Orbital Degeneracy

Abstract

The isotropic limit of spin systems with orbital degeneracy is shown to have global SU(4) symmetry. On many 2D lattices, the ground state does not posses long range order, which may explain the observed spin liquid properties of $LiNi{O}_2$. In the SU(4) Neel ordered state, spin-spin correlations can be antiferromagneitc between two neighboring sites with parallel magnetic moments.

11 pages, 2 figures. submitted to PRL

Cited by in corpus (202)

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• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Orbital liquid in three dimensional Mott insulator: $LaTi{O}_3$
• Exotic phases induced by strong spin-orbit coupling in ordered double perovskites
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Spin Order due to Orbital Fluctuations: Cubic Vanadates
• Spin-orbital quantum liquid on the honeycomb lattice
• One-Dimensional Magnetism
• Phase diagram of the half-filled two-dimensional SU(N) Hubbard-Heisenberg model: a quantum Monte Carlo study
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• Thermodynamics of the one-dimensional SU(4) symmetric spin-orbital model
• Two-band model for magnetism and superconductivity in nickelates
• Antiferromagnetic spin correlation of SU($\mathcal{N}$) Fermi gas in an optical super-lattice
• Spin-Orbital Entanglement and Violation of the Goodenough-Kanamori Rules
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Phase diagram of a 1 dimensional spin-orbital model
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Topological liquids and valence cluster states in two-dimensional SU(N) magnets
• Orbital ordering in frustrated Jahn-Teller systems
• Orbital degeneracy as a source of frustration in LiNiO${}_2$
• Emergent $\mathrm{SU}(4)$ Symmetry in $\alpha$-ZrCl${}_3$ and Crystalline Spin-Orbital Liquids
• Order from disorder: Quantum spin gap in magnon spectra of LaTiO_3
• SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
• Orbital order in classical models of transition-metal compounds
• Spin--orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model
• Quantum melting of magnetic long-range order near orbital degeneracy. Classical phases and Gaussian fluctuations
• Exact Diagonalization of Heisenberg SU(N) models
• Exact solution of a spin-ladder model
• A Z${}_2$ spin-orbital liquid state in the square lattice Kugel-Khomskii model
• Orbital and spin physics in LiNiO2 and NaNiO2
• Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds
• Frustration and entanglement in the $t_{2g}$ spin--orbital model on a triangular lattice: valence--bond and generalized liquid states
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• Quantum Phase Transition in the SU(4) Spin-Orbital Model on the Triangular Lattice
• Exact spontaneous plaquette ground states for high-spin ladder models
• Interlayer Magnetic Frustration in Quasi-stoichiometric Li1-xNi1+xO2
• Emergent honeycomb lattice in LiZn2Mo3O8
• Spontaneous plaquette formation in the SU(4) Spin-Orbital ladder
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields
• Numerical Study of the One-Dimensional Spin-Orbit Coupled System with SU(2)$\otimes$SU(2) Symmetry
• Effect of symmetry breaking perturbations in the one-dimensional SU(4) spin-orbital model
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: implications for twistronics and Mott insulators
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
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• Competing Ordered States in Bilayer Graphene
• Ground State and Excitations of Spin Chain with Orbital Degeneracy
• Ordering and Spin Waves in NaNiO2 : A Stacked Quantum Ferromagnet
• Entropy Driven Dimerization in a One-Dimensional Spin-Orbital Model
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Spin liquid ground state in a two dimensional non-frustrated spin model
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
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• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry
• Equation of State and Thermometry of the 2D SU($N$) Fermi-Hubbard Model
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• Maximized Orbital and Spin Kondo effects in a single-electron transistor
• Sensitivity of the Mott Transition to Non-cubic Splitting of the Orbital Degeneracy: Application to NH3 K3C60
• SU(4)-symmetric spin-orbital liquids on the hyperhoneycomb lattice
• Resonating singlet valence plaquettes
• Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model
• Spin-Orbital Entanglement and Phase Diagram of Spin-orbital Chain with $SU(2)\times SU(2)$ Symmetry
• Magnetization transport in spin ladders and next-nearest-neighbor chains
• Competing phases and topological excitations of spin-one pyrochlore antiferromagnets
• Entanglement and corner Hamiltonian spectra of integrable open spin chains
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Topological Order in an Entangled SU(2)$\otimes$XY Spin-Orbital Ring
• Competing Orders and Hidden Duality Symmetries in Two-leg Spin Ladder Systems
• Dynamical Jahn-Teller Effect in Spin-Orbital Coupled System
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Elementary excitations of the symmetric spin-orbital model: The XY limit
• Fractionalization, entanglement, and separation: understanding the collective excitations in a spin-orbital chain
• Paraorbital ground state of trivalent Ni ion in LiNiO${}_2$ from DFT+DMFT calculations
• Stability of the spin-$1/2$ kagome ground state with breathing anisotropy
• Emergent Fermi surface in a triangular-lattice SU(4) quantum antiferromagnet
• Phases of the generalized two-leg spin ladder: A view from the SU(4) symmetry
• Two-dimensional gapless spin liquids in frustrated SU(N) quantum magnets
• Dynamics of a j=3/2 quantum spin liquid
• Exact dynamical structure factor of the degenerate Haldane-Shastry model
• Ordered valence bond states in symmetric two-dimensional spin-orbital systems
• Theory for high spin systems with orbital degeneracy
• Tetramerization in a SU(4)-Heisenberg model on the honeycomb lattice
• Wigner crystal phases in confined carbon nanotubes
• Elementary excitations in one-dimensional spin-orbital models: neutral and charged solitons and their bound states
• Continuous phase transition between Neel and valence bond solid phases in a J-Q-like spin ladder system
• Crossover Phenomena in the One-Dimensional SU(4) Spin-Orbit Model under Magnetic Fields
• How spin-orbital entanglement depends on the spin-orbit coupling in a Mott insulator
• Frustrated Magnetism in Mott Insulating (V${}_{1-x}$Cr${}_x$)${}_2$O${}_3$
• Exact Dynamics of the SU(K) Haldane-Shastry Model
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Planar spin exchange in LiNiO_2
• Magnetic excitations in one-dimensional spin-orbital models
• Unveiling a critical stripy state in the triangular-lattice SU(4) spin-orbital model
• Featureless quantum paramagnet with frustrated criticality and competing spiral magnetism on spin-1 honeycomb lattice magnet
• Effective field theory for Sp(N) antiferromagnets and its phase structure
• Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model
• Charge and orbital order in transition metal oxides
• Coloron excitations of the SU(3) Haldane--Shastry model
• Twisting the Dirac cones of the SU(4) spin-orbital liquid on the honeycomb lattice
• Thermodynamics of a one-dimensional S=1/2 spin-orbital model
• Dynamical Properties of Spin-Orbital Chains in a Magnetic Field
• Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions
• Plaquette Ordering in SU(4) Antiferromagnets
• The ordering of energy levels for SU(n) symmetric antiferromagnetic chains
• Two-leg SU(2n) spin ladder: A low-energy effective field theory approach
• Quantum Melting of Magnetic Order in an Organic Dimer-Mott Insulating System
• SU(4)-symmetric Hubbard model at quarter filling: Insights from the dynamical mean-field approach
• Dissipative remote-state preparation in an interacting medium
• Gapless to gapless phase transitions in quantum spin chains
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• Spin-orbital exchange of strongly interacting fermions on the $p$-band of a two-dimensional optical lattice
• Magnetic properties of an SU(4) spin-orbital chain
• Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry
• Entanglement Driven Phase Transitions in Spin-Orbital Models
• Spin-Orbital Entangled Liquid State in the Copper Oxide Ba${}_3$CuSb${}_2$O${}_9$
• Spin, orbital and topological order in models of strongly correlated electrons
• Spatial fluctuations of spin and orbital in two-orbital Hubbard model
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits
• Series study of the One-dimensional S-T Spin-Orbital Model
• Generalized Valence Bond State and Solvable Models for Spin-1/2 Systems with Orbital degeneracy
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
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• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• Frustrated Kondo impurity triangle: A simple model of deconfinement
• Symmetry breaking in low-dimensional SU(N) antiferromagnets
• Linear Flavor-Wave Analysis of SU(4)-Symmetric Tetramer Model with Population Imbalance
• Spin nematics in frustrated spin-dimer systems with bilayer structure
• Dimer description of the SU(4) antiferromagnet on the triangular lattice
• Effects of a magnetic field on the one-dimensional spin-orbital model
• Theory for spin and orbital orderings in high temperature phase in $YV{O}_3$
• Spin, charge, and orbital correlations in the one-dimensional t2g-orbital Hubbard model
• Complementary colors of colorons: the elementary excitations of the SU(3) Haldane--Shastry model
• Orbital Ordering and Orbital Fluctuations in Transition Metal Oxides
• Quantum phase diagram of an exactly solved mixed spin ladder
• Tunable exciton valley-pseudospin orders in moiré Bose-Hubbard model
• Symmetries in the Hubbard model with n-fold orbital degeneracy
• Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model
• Two-orbital physics of high spin fermionic alkaline earth atoms confined in a one-dimensional chain
• Quantum criticality of vanadium chains with strong relativistic spin-orbit interaction
• Mean-field Study of Charge, Spin, and Orbital Orderings in Triangular-lattice Compounds ANiO2 (A=Na, Li, Ag)
• Effect of Hund's rule coupling on SU(4) spin-orbital system
• Formation of energy gap in higher dimensional spin-orbital liquids
• Phase Diagram of the Spin-Orbital model on the Square Lattice
• Designing Quantum Spin-Orbital Liquids in Artificial Mott Insulators
• Orbital Dzyaloshinskii-Moriya Exchange Interaction
• One dimensional model for doubly degenerate electrons
• SU(4) Spin-Orbital Two-Leg Ladder, Square and Triangle Lattices
• Spin and orbital valence bond solids in a one-dimensional spin-orbital system: Schwinger boson mean field theory
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Response functions in multicomponent Luttinger liquids
• Charge Kondo effect toward a non-Fermi-liquid fixed point in the orbitally degenerate exchange model
• Canted antiferromagnetism in a spin-orbit coupled $S_{\text{eff}}=3/2$ triangular-lattice magnet DyAuGe
• Theory of electrons with orbital degeneracy
• Spin-valley magnetism on the triangular moiré lattice with SU(4) breaking interactions
• Contractor renormalization group theory of the SU($N$) chains and ladders
• Spin-orbital gapped phase with least symmetry breaking in the one-dimensional symmetrically coupled spin-orbital model
• Exact solution and magnetic properties of an anisotropic spin ladder
• Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
• Phase diagram and symmetry breaking of SU(4) spin-orbital chain in a generalized external field
• Magnetization plateau and quantum phase transitions in a spin-orbital model
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Anisotropic excitonic magnetism from discrete ${\mathrm{C}}_4$ symmetry in CeRhIn${}_5$
• Non linear sigma models and quantum spin systems
• The excitations of the sympletic integrable models and their applications
• Quantum phases of collective SU(3) spin systems with bipartite symmetry
• Magnetic and orbital instabilities in a lattice of SU(4) organometallic Kondo complexes
• Mott insulating states of the anisotropic SU(4) Dirac fermions
• Spin-orbital liquid in Ba${}_3$CuSb${}_2$O${}_9$ stabilized by oxygen holes
• A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group
• Doping a Mott insulator with orbital degrees of freedom
• On the ground state and excitations of a four-component fermion model
• Deformation of SU(4) singlet spin-orbital state due to Hund's rule coupling
• Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model
• Upper branch thermal Hall effect in quantum paramagnets
• Crossover between Fermi Liquid and non-Fermi Liquid in Orbitally Degenerate Kondo Systems
• Bethe ansatz for the SU(4) extension of the Hubbard Model
• Ring-exchange interaction in doubly degenerate orbital system
• Phase transition in a magnetic field in V2-yO3 (y=0 and 0.04)
• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• Lowest energy states of an $O(N)$ fermionic chain
• Flavor Nernst effects in quantum paramagnets
• $p$ orbitals in 3D lattices; fermions, bosons and (exotic) models of magnetism
• Order by disorder in a four flavor Mott-insulator on the fcc lattice
• Dynamically generated dimension reduction and crossover in a spin orbital model
• Multiband effects on the conductivity for a multiband Hubbard model
• Non-Landau Quantum Phase Transitions and nearly-Marginal non-Fermi Liquid
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice
• Gutzwiller approximation approach to the SU(4) $t$-$J$ model
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Spontaneous Currents in Spinless Fermion Lattice Models at the Strong-Coupling Limit
• Subsystem symmetries, critical Bose surface, and immobile excitations in an extended compass model
• Phase transition and critical properties of spin-orbital interacting systems
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model