Variational Monte Carlo approach to the SU(4) spin-orbital model on the triangular lattice

Previous investigations have suggested that the simplest spin-orbital model on the simplest frustrated lattice can host a nematic quantum spin-orbital liquid state. Namely, the orbital degeneracy of the SU (4) Kugel-Khomskii model tends to enhance quantum fluctuations and stabilize a quantum spin-orbital liquid exhibiting stripy features on the triangular lattice, as revealed by the state-of-the-art method of the density matrix renormalization group boosted by Gutzwiller projected wave functions. In this work, using the variational quantum Monte Carlo method, we study several spin-orbital liquid states, including a uniform -flux state, three stripy states, and a plaquette state, on the L torus up to L=24. It turns out that one of these stripy states, called the ``stripe-II'' state, is energetically favored. This ground state breaks the C₆ symmetry of the lattice, resulting in a reduced C₂ symmetry and doubled unit cells while preserving the SU (4) spin-orbital rotation symmetry. Such a nematic quantum spin-orbital liquid state can be characterized by a parton Fermi surface (FS) consisting of open orbits in the Brillouin zone, in contrast to the circular FS of the uniform -flux state.