Orbital polarization-driven quantum spin-orbital liquid in an SU(4) model

The SU(4) symmetric Kugel-Khomskii model of Mott insulators has previously been suggested to host a quantum spin-orbital liquid (QSOL) ground state on the honeycomb lattice. It has been reported that QSOLs host not only spinon excitations but also fractionalized orbital excitations. However, in general, the hopping amplitudes between different orbitals are unequal, which drives the system away from the isotropic SU(4) Kugel–Khomskii model and generates compass-type pseudospin interaction terms. We first show a microscopic theory to obtain a generic nearest neighbor spin-orbital model which includes bond-dependent pseudospin interactions and other terms through direct-exchange hopping. We will present the phase diagram of our model using a combination of numerical techniques, including classical Monte Carlo simulations, linear flavor-wave theory, and exact diagonalization. Our findings reveal a broad, stable region surrounding the SU(4) spin–orbital liquid ground state, as well as an orbital-polarization–driven QSOL that emerges from the interplay between frustrated orbital exchange and orbital polarization terms.