The variational discrete action theory (VDAT) at $\mathcal{N}=3$ is a potent tool for accurately capturing Mott and Hund physics at zero temperature in $d=\infty$ at a cost comparable to the Gutzwiller approximation, which is recovered by VDAT at $\mathcal{N}=2$. Here we develop a qubit parametrization of the gauge constrained algorithm of VDAT at $\mathcal{N}=3$ for the multiorbital Hubbard model with general density-density interactions. The qubit parametrization yields an explicit variational trial energy, and the variational parameters consist of the momentum density distribution, the shape of a reference fermi surface, and the pure state of a qubit system with dimension of the local Hilbert space. To illustrate the power of the qubit parametrization, we solve for the ground-state properties of the multiorbital Hubbard model with Hund coupling for local orbital number $N_{\text{orb}}=2–7$. A Taylor series expansion of the partially optimized trial energy is used to explain how the Hund's coupling changes the order of the Mott transition. For the case of the $SU\left(2N_{\text{orb}}\right)$ Hubbard model, an explicit approach for computing the critical $U_c$ for the Mott transition is provided, yielding an analytical expression for $U_c$ in the large $N_{\text{orb}}$ limit. Additionally, we provide an analytical solution for the ground-state properties of the single-band Hubbard model with a special density of states. Finally, we demonstrate that the qubit parametrization can also be applied to $\mathcal{N}=2$, for both G-type and B-type variants, where the G-type yields an identical expression to the slave spin mean-field theory. The qubit parametrization not only improves the efficiency and transparency of VDAT at $\mathcal{N}=3$, but also provides the key advances for the construction of a one-body reduced density matrix functional capable of capturing Mott and Hund physics.

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• Mott insulators
• Green's function methods
• Hubbard model
• Variational approach