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While the enhancement of the spin-space symmetry from the usual$\mathrm{SU}(2)$ to $\mathrm{SU}(N)$ is promising for finding nontrivialquantum spin liquids, its realization in magnetic materials remainschallenging. Here we propose a new mechanism by which the $\mathrm{SU}(4)$symmetry emerges in the strong spin-orbit coupling limit. In $d^1$ transitionmetal compounds with edge-sharing anion octahedra, the spin-orbit couplinggives rise to strongly bond-dependent and apparently $\mathrm{SU}(4)$-breakinghopping between the $J_\textrm{eff}=3/2$ quartets. However, in the honeycombstructure, a gauge transformation maps the system to an$\mathrm{SU}(4)$-symmetric Hubbard model. In the strong repulsion limit atquarter filling, as realized in $\alpha$-ZrCl$_3,$ the low-energy effectivemodel is the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice, whichcannot have a trivial gapped ground state and is expected to host a gaplessspin-orbital liquid. By generalizing this model to other three-dimensionallattices, we also propose crystalline spin-orbital liquids protected by thisemergent $\mathrm{SU}(4)$ symmetry and space group symmetries.

Emergent $\mathrm{SU}(4)$ Symmetry in $\alpha$-ZrCl$_3$ and Crystalline Spin-Orbital Liquids