$\textit{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications

In this study, we introduce a novel implementation of density functional theory integrated with single-site dynamical mean-field theory to investigate the complex properties of strongly correlated materials. This comprehensive first-principles many-body computational toolkit, termed $\texttt{Zen}$, utilizes the Vienna $\textit{ab initio}$ simulation package and the $\texttt{Quantum ESPRESSO}$ code to perform density functional theory calculations and generate band structures for realistic materials. The challenges associated with correlated electron systems are addressed through two distinct yet complementary quantum impurity solvers: the natural orbitals renormalization group solver for zero temperature and the hybridization expansion continuous-time quantum Monte Carlo solver for finite temperature. Additionally, this newly developed toolkit incorporates several valuable post-processing tools, such as $\texttt{ACFlow}$, which employs the maximum entropy method and the stochastic pole expansion method for the analytic continuation of Matsubara Green's functions and self-energy functions. To validate the performance of this toolkit, we examine three representative cases: the correlated metal SrVO$_{3}$, the nickel-based unconventional superconductor La$_{3}$Ni$_{2}$O$_{7}$, and the wide-gap Mott insulator MnO. The results obtained demonstrate strong agreement with experimental findings and previously available theoretical results. Notably, we successfully elucidate the quasiparticle peak and band renormalization in SrVO$_{3}$, the dominance of Hund correlation in La$_{3}$Ni$_{2}$O$_{7}$, and the pressure-driven insulator-metal transition as well as the high-spin to low-spin transition in MnO. These findings suggest that $\texttt{Zen}$ is proficient in accurately describing the electronic structures of $d$-electron correlated materials.