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

TL;DR

This paper introduces a method to derive low-energy Hubbard-like Hamiltonians from ab initio Quantum Monte Carlo data, enabling accurate modeling of molecules and solids without experimental inputs.

Contribution

The paper presents ab initio density matrix downfolding (AIDMD), a novel approach to extract effective Hamiltonians directly from quantum Monte Carlo calculations.

Findings

Accurately reproduces energy gaps in benzene without experimental data.

Estimates the Hubbard U*/t ratio for graphene as 1.3 ± 0.2.

Enables calculation of excited states in molecules and large-scale lattice models for solids.

Abstract

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio Quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding (AIDMD). For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard $U^{*}/t$ to be $1.3 \pm 0.2$, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large scale calculations using techniques designed for lattice models.