# 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 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. 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{sup ∗}/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.

- Authors:

- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green St., Urbana, Illinois 61801 (United States)

- Publication Date:

- OSTI Identifier:
- 22489553

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COMPARATIVE EVALUATIONS; DENSITY MATRIX; EXCITED STATES; GRAPHENE; GROUND STATES; HAMILTONIANS; MONTE CARLO METHOD; RANDOM PHASE APPROXIMATION; SOLIDS; WAVE FUNCTIONS

### Citation Formats

```
Changlani, Hitesh J., Zheng, Huihuo, and Wagner, Lucas K.
```*Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions*. United States: N. p., 2015.
Web. doi:10.1063/1.4927664.

```
Changlani, Hitesh J., Zheng, Huihuo, & Wagner, Lucas K.
```*Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions*. United States. doi:10.1063/1.4927664.

```
Changlani, Hitesh J., Zheng, Huihuo, and Wagner, Lucas K. Mon .
"Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions". United States. doi:10.1063/1.4927664.
```

```
@article{osti_22489553,
```

title = {Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions},

author = {Changlani, Hitesh J. and Zheng, Huihuo and Wagner, Lucas K.},

abstractNote = {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. 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{sup ∗}/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.},

doi = {10.1063/1.4927664},

journal = {Journal of Chemical Physics},

number = 10,

volume = 143,

place = {United States},

year = {Mon Sep 14 00:00:00 EDT 2015},

month = {Mon Sep 14 00:00:00 EDT 2015}

}