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.

4.5 page main text + supplementary materials. Science Bulletin (2022)

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• U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection
• Quantum spin liquid from electron-phonon coupling
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Canted antiferromagnetism in a spin-orbit coupled $S_{\text{eff}}=3/2$ triangular-lattice magnet DyAuGe
• 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
• Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model