Title: Emergent $\mathrm{SU}(4)$ Symmetry in $α$-ZrCl$_3$ and Crystalline Spin-Orbital Liquids,
Abstract: While the enhancement of the spin-space symmetry from the usual
$\mathrm{SU}(2)$ to $\mathrm{SU}(N)$ is promising for finding nontrivial
quantum spin liquids, its realization in magnetic materials remains
challenging. Here we propose a new mechanism by which the $\mathrm{SU}(4)$
symmetry emerges in the strong spin-orbit coupling limit. In $d^1$ transition
metal compounds with edge-sharing anion octahedra, the spin-orbit coupling
gives rise to strongly bond-dependent and apparently $\mathrm{SU}(4)$-breaking
hopping between the $J_\textrm{eff}=3/2$ quartets. However, in the honeycomb
structure, a gauge transformation maps the system to an
$\mathrm{SU}(4)$-symmetric Hubbard model. In the strong repulsion limit at
quarter filling, as realized in $\alpha$-ZrCl$_3,$ the low-energy effective
model is the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice, which
cannot have a trivial gapped ground state and is expected to host a gapless
spin-orbital liquid. By generalizing this model to other three-dimensional
lattices, we also propose crystalline spin-orbital liquids protected by this
emergent $\mathrm{SU}(4)$ symmetry and space group symmetries.