Precise ground state of multi-orbital Mott systems via the variational discrete action theory

Abstract

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

14 pages, 5 figures

References in corpus (12)

• The density-matrix renormalization group in the age of matrix product states
• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Real time evolution using the density matrix renormalization group
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Spin freezing transition and non-Fermi-liquid self-energy in a 3-orbital model
• High-spin to low-spin and orbital polarization transitions in multiorbital Mott systems
• Metal-Insulator phase diagram and orbital selectivity in 3-orbital models with rotationally invariant Hund coupling
• Effect of Crystal-Field Splitting and Inter-Band Hybridization on the Metal-Insulator Transitions of Strongly Correlated Systems
• Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension
• In-gap band in the one-dimensional two-orbital Kanamori-Hubbard model with inter-orbital Coulomb interaction

Cited by in corpus (4)

• Magnetism and Metallicity in Moiré Transition Metal Dichalcogenides
• Constructive Fermionic Matrix Product States for Projected Fermi Sea
• Density-Matrix Mean-Field Theory
• Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice