Precise ground state of multiorbital Mott systems via the variational discrete action theory

Determining the ground state of multi-orbital Hubbard models is critical for understanding strongly correlated electron materials, yet existing methods struggle to simultaneously reach zero temperature and infinite system size. The \textit{de facto} standard approximate a finite dimension model with $d=\infty$ version, which can then be formally solved via dynamical mean-field theory (DMFT), though DMFT solution limited by unbiased impurity solvers multiple orbitals. recently developed variational discrete action (VDAT) offers new approach solve model, ansatz that controlled an integer $\mathcal{N}$, monotonically approaches exact at increasing computational cost. Here we propose decoupled minimization algorithm implement VDAT in study $\mathcal{N}=2-4$ . At $\mathcal{N}=2$, rigorously recovers Gutzwiller approximation, reproducing known results. $\mathcal{N}=3$, precisely captures competition between $U$, Hund $J$, crystal field $\Delta$ two orbital over all parameter space, negligible For sufficiently large $U/t$ $J/U$, show drives first-order transition within Mott insulating regime. In polarization limit find interactions have nontrivial effect even small $U/t$. will far ranging implications Hamiltonians materials.