A Z${}_2$ spin-orbital liquid state in the square lattice Kugel-Khomskii model

Abstract

We argue for the existence of a liquid ground state in a class of square lattice models of orbitally degenerate insulators. Starting with the SU(4) symmetric Kugel-Khomskii model, we utilize a Majorana Fermion representation of spin-orbital operators to access novel phases. Variational wavefunctions of candidate liquid phases are thus obtained, whose properties are evaluated using Variational Monte Carlo. These states are disordered, and are found to have excellent energetics and ground state overlap ($>40$) when compared with exact diagonalization on 16 site clusters. We conclude that these are spin-orbital liquid ground states with emergent nodal fermions and Z${}_2$ gauge fields. Connections to spin 3/2 cold atom systems and properties in the absence of SU(4) symmetry are briefly discussed.

arXiv comment9 pages, 4 figures, 3 tables, published version

References in corpus (15)

• Anyons in an exactly solved model and beyond
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Degenerate Fermi Gases of Ytterbium
• Quantum Melting of Magnetic Order due to Orbital Fluctuations
• SU(4) Theory for Spin Systems with Orbital Degeneracy
• Orbital liquid in three dimensional Mott insulator: $LaTi{O}_3$
• Spin and orbital frustration in MnSc_2S_4 and FeSc_2S_4
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Interplay of Mott Transition and Ferromagnetism in the Orbitally Degenerate Hubbard Model
• Alternating Spin and Orbital Dimerization in Strong-coupling Two-band Models
• A Mott Insulator of Ultracold Alkaline-Earth-Like Atoms
• Plaquette Ground State in the Two-dimensional SU(4) Spin-Orbital Model
• Projected wave functions for fractionalized phases of quantum spin systems
• Plaquette Ordering in SU(4) Antiferromagnets
• Formation of energy gap in higher dimensional spin-orbital liquids

Cited by in corpus (58)

• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Spin-orbital quantum liquid on the honeycomb lattice
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices
• Topological liquids and valence cluster states in two-dimensional SU(N) magnets
• Emergent $\mathrm{SU}(4)$ Symmetry in $\alpha$-ZrCl${}_3$ and Crystalline Spin-Orbital Liquids
• Vison states and confinement transitions of Z2 spin liquids on the kagome lattice
• Exact Diagonalization of Heisenberg SU(N) models
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
• Flat band in twisted bilayer Bravais lattices
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Chiral spin-orbital liquids with nodal lines
• Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids
• Noncollinear Magnetic Order Stabilized by Entangled Spin-Orbital Fluctuations
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry
• SU(4)-symmetric spin-orbital liquids on the hyperhoneycomb lattice
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• Topological Order in an Entangled SU(2)$\otimes$XY Spin-Orbital Ring
• SU(2)-invariant Majorana spin liquid with stable parton Fermi surfaces in an exactly solvable model
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Linear Flavor-Wave Theory for Fully Antisymmetric $\mathrm{SU}(N)$ Irreducible Representations
• Dynamics of a j=3/2 quantum spin liquid
• Majorana Spin Liquids on a two-leg ladder
• Dynamics of a two-dimensional quantum spin-orbital liquid: spectroscopic signatures of fermionic magnons
• Kitaev spin-orbital bilayers and their moiré superlattices
• Tetramerization in a SU(4)-Heisenberg model on the honeycomb lattice
• Phase diagram of the square lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Vison crystals, chiral and crystalline phases in the Yao-Lee model
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• $\mathrm{SU}(4)$-Symmetric Quantum Spin-Orbital Liquids on Various Lattices
• Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model
• Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions
• Twisting the Dirac cones of the SU(4) spin-orbital liquid on the honeycomb lattice
• Twisted bilayer BC${}_3$: Valley interlocked anisotropic flat bands
• Exploring spin-orbital models with dipolar fermions in zig-zag optical lattices
• Spin-orbital exchange of strongly interacting fermions on the $p$-band of a two-dimensional optical lattice
• Magnetic phases of spin-3/2 fermions on a spatially anisotropic square lattice
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Elementary Excitations in the Symmetric Spin--Orbital Model
• Dimer description of the SU(4) antiferromagnet on the triangular lattice
• Designing Quantum Spin-Orbital Liquids in Artificial Mott Insulators
• Finite size effects in the Z_2 spin liquid on the kagome lattice
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Ferromagnetic spin-orbital liquid of dipolar fermions in zigzag lattices
• Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model
• Photo-induced charge, spin, and orbital order in the two-orbital extended Hubbard model
• Order by disorder in a four flavor Mott-insulator on the fcc lattice
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems
• Three-dimensional spin-orbital liquids
• Majorana Diagrammatics for Quantum Spin-1/2 Models
• Realization of Nearly Dispersionless Bands with Strong Orbital Anisotropy from Destructive Interference in Twisted Bilayer MoS2
• The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach