Unveiling a critical stripy state in the triangular-lattice SU(4) spin-orbital model

Abstract

The simplest spin-orbital model can host a nematic spin-orbital liquid state on the triangular lattice. We provide clear evidence that the ground state of the SU(4) Kugel-Khomskii model on the triangular lattice can be well described by a "single" Gutzwiller projected wave function with an emergent parton Fermi surface, despite it exhibits strong finite-size effect in quasi-one-dimensional cylinders. The finite-size effect can be resolved by the fact that the parton Fermi surface consists of open orbits in the reciprocal space. Thereby, a stripy liquid state is expected in the two-dimensional limit, which preserves the SU(4) symmetry while breaks the translational symmetry by doubling the unit cell along one of the lattice vector directions. It is indicative that these stripes are critical and the central charge is $c=3$, in agreement with the SU(4)${}_1$ Wess-Zumino-Witten conformal field theory. All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.

arXiv comment4.5 page main text + supplementary materials. Science Bulletin (2022)

References in corpus (49)

• Entanglement in quantum critical phenomena
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• Quantum Spin Liquid States
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Quantum Spin Liquids
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• Lieb-Schultz-Mattis in Higher Dimensions
• A Field Guide to Spin Liquids
• Topological Superconductivity in Twisted Multilayer Graphene
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Neel order in square and triangular lattice Heisenberg models
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• 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: $LaTi{O}_3$
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Spin-orbital quantum liquid on the honeycomb lattice
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Alternating Spin and Orbital Dimerization in Strong-coupling Two-band Models
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice
• Emergent $\mathrm{SU}(4)$ Symmetry in $\alpha$-ZrCl${}_3$ and Crystalline Spin-Orbital Liquids
• SU(4) chiral spin liquid, exciton supersolid and electric detection in moiré bilayers
• Bridging Hubbard Model Physics and Quantum Hall Physics in Trilayer Graphene/h-BN moiré superlattice
• Orbital frustration at the origin of the magnetic behavior in LiNiO2
• Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder
• Exact spontaneous plaquette ground states for high-spin ladder models
• Quantum Phase Transition in the SU(4) Spin-Orbital Model on the Triangular Lattice
• Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields
• DMRG studies of critical SU(N) spin chains
• Spontaneous plaquette formation in the SU(4) Spin-Orbital ladder
• Plaquette Ground State in the Two-dimensional SU(4) Spin-Orbital Model
• Spin-valley density wave in moiré materials
• SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: implications for twistronics and Mott insulators
• Ground State and Excitations of Spin Chain with Orbital Degeneracy
• Tensor network representations of parton wave functions
• Detection and characterization of symmetry-broken long-range orders in the spin-$\frac{1}{2}$ triangular Heisenberg model
• Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
• Efficient tensor network representation for Gutzwiller projected states of paired fermions
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Density matrix renormalization group boosted by Gutzwiller projected wave functions
• Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators
• Emergent Fermi surface in a triangular-lattice SU(4) quantum antiferromagnet
• $\mathrm{SU}(4)$-Symmetric Quantum Spin-Orbital Liquids on Various Lattices

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• Thermodynamic signature of the $\mathrm{SU}(4)$ spin-orbital liquid and symmetry fractionalization from the Lieb-Schultz-Mattis theorem
• A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group
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