Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

Area of Science:

• Computational Chemistry
• Condensed Matter Physics
• Quantum Mechanics

Background:

• Deriving accurate low-energy effective Hamiltonians is crucial for understanding molecular and solid-state properties.
• Ab initio methods provide a foundation for theoretical calculations but can be computationally expensive for large systems.

Purpose of the Study:

• To introduce a novel method, ab initio density matrix based downfolding, for obtaining effective Hubbard-like model Hamiltonians.
• To validate the method's accuracy for both finite molecular systems and extended solid systems.

Main Methods:

• Utilizing ab initio quantum Monte Carlo calculations to obtain ground and excited state energies and two-body density matrices.
• Fitting Hamiltonian parameters to match ab initio data, a process termed density matrix based downfolding.
• Applying the method to benzene and graphene as test cases.

Main Results:

• Achieved good agreement with experimental energy gaps for benzene without empirical inputs.
• Determined an effective on-site Hubbard U(∗)/t of 1.3 ± 0.2 for graphene, consistent with other advanced methods.
• Demonstrated the capability to calculate excited states for molecules and enable large-scale simulations for solids.

Conclusions:

• Ab initio density matrix based downfolding is a reliable approach for generating effective Hamiltonians.
• This method bridges the gap between high-accuracy ab initio calculations and computationally tractable model Hamiltonians.
• The approach facilitates advanced studies of electronic properties in both molecular and condensed matter systems.