Hidden spin-orbital hexagonal ordering induced by strong correlations in LiVS2

We develop a versatile first-principles many-body scheme for multiorbital lattice susceptibilities including full frequency-dependent local vertex effects and investigate the different instabilities in the metallic phase of the quasi-two-dimensional compound ${\mathrm{LiVS}}_{2}$. Application of such advanced correlated electronic structure methods for the ${t}_{2g}$ subspace reveals a highly entangled spin-orbital hexagonal ordering bringing about an inherently intersite order parameter for the trimerization transition. The importance of such nontrivial ordering towards the formation of intriguing insulating phases at low temperatures is discussed.