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

Abstract

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo (QMC) 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 ± 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.

Toward a predictive theory of correlated materials

“…QMC methods now also have better access to excited states and are becoming capable of diagnosing when GW methods are best applied (82). Determining more accurately the effective Hubbard parameters that enter LDA+DMFT is another outstanding challenge to which QMC may contribute in the future (83).…”

Erratum: Computation of the Correlated Metal-Insulator Transition in Vanadium Dioxide from First Principles [Phys. Rev. Lett. 114 , 176401 (2015)]

“…Therefore, the singlet-triplet excitation is J ¼ 492ð24Þ meV, within two statistical error bars of the experimental result. This realization was made possible by work we have done regarding effective model fitting [3,4]. We view this as a strong motivation to have a rigorous theory of effective models as we tried to lay out in those papers.…”

Inverse statistical problems: from the inverse Ising problem to data science

“…In physics, inverse statistical problems also arise when we need to design a many-body system with particular desired properties. Examples are finding the potentials that result in a particular single-particle distribution [48,122], interaction parameters in a binary alloy that yield the observed correlations [142], the potentials between atoms that lead to specific crystal lattices [253], or the parameters of a Hamiltonian that lead to a particular density matrix [47]. In the context of soft matter, a question is how to design a many-body system that will self-assemble into a particular spatial configuration or has particular bulk properties [185,227].…”