# Auxiliary-Field Quantum Monte Carlo Simulations of Strongly-Correlated Molecules and Solids

## Abstract

We propose a method of implementing projected wave functions for second-quantized auxiliary-field quantum Monte Carlo (AFQMC) techniques. The method is based on expressing the two-body projector as one-body terms coupled to binary Ising fields. To benchmark the method, we choose to study the two-dimensional (2D) one-band Hubbard model with repulsive interactions using the constrained-path MC (CPMC). The CPMC uses a trial wave function to guide the random walks so that the so-called fermion sign problem can be eliminated. The trial wave function also serves as the importance function in Monte Carlo sampling. As such, the quality of the trial wave function has a direct impact to the efficiency and accuracy of the simulations.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1335769

- Report Number(s):
- LLNL-SR-708821

TRN: US1701387

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; WAVE FUNCTIONS; MONTE CARLO METHOD; COMPUTERIZED SIMULATION; HUBBARD MODEL; TWO-DIMENSIONAL SYSTEMS; CORRELATIONS; TWO-BODY PROBLEM; MOLECULES; RANDOMNESS; SOLIDS; ACCURACY; BENCHMARKS; EFFICIENCY; PROJECTION OPERATORS; SECOND QUANTIZATION; IMPLEMENTATION

### Citation Formats

```
Chang, C., and Morales, M. A..
```*Auxiliary-Field Quantum Monte Carlo Simulations of Strongly-Correlated Molecules and Solids*. United States: N. p., 2016.
Web. doi:10.2172/1335769.

```
Chang, C., & Morales, M. A..
```*Auxiliary-Field Quantum Monte Carlo Simulations of Strongly-Correlated Molecules and Solids*. United States. doi:10.2172/1335769.

```
Chang, C., and Morales, M. A.. Thu .
"Auxiliary-Field Quantum Monte Carlo Simulations of Strongly-Correlated Molecules and Solids". United States. doi:10.2172/1335769. https://www.osti.gov/servlets/purl/1335769.
```

```
@article{osti_1335769,
```

title = {Auxiliary-Field Quantum Monte Carlo Simulations of Strongly-Correlated Molecules and Solids},

author = {Chang, C. and Morales, M. A.},

abstractNote = {We propose a method of implementing projected wave functions for second-quantized auxiliary-field quantum Monte Carlo (AFQMC) techniques. The method is based on expressing the two-body projector as one-body terms coupled to binary Ising fields. To benchmark the method, we choose to study the two-dimensional (2D) one-band Hubbard model with repulsive interactions using the constrained-path MC (CPMC). The CPMC uses a trial wave function to guide the random walks so that the so-called fermion sign problem can be eliminated. The trial wave function also serves as the importance function in Monte Carlo sampling. As such, the quality of the trial wave function has a direct impact to the efficiency and accuracy of the simulations.},

doi = {10.2172/1335769},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Nov 10 00:00:00 EST 2016},

month = {Thu Nov 10 00:00:00 EST 2016}

}

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