# Symmetry projected Jastrow mean field wavefunction in variational Monte Carlo

## TL;DR

This paper introduces an extension of variational Monte Carlo methods to optimize symmetry-projected Jastrow mean field wavefunctions, enabling efficient treatment of complex correlated quantum systems with multiple symmetries.

## Contribution

The authors develop a low-scaling VMC algorithm for optimizing symmetry-projected Jastrow mean field wavefunctions, including various advanced wavefunction forms like JAGP and RVB, with applications to benchmark systems.

## Key findings

- Significant correlation energy captured in benchmark systems.
- Efficient optimization with multiple broken symmetries.
- Ability to compute reduced density matrices and other observables.

## Abstract

We extend our low-scaling variational Monte Carlo (VMC) algorithm to optimize the symmetry projected Jastrow mean field (SJMF) wavefunctions. These wavefunctions consist of a symmetry-projected product of a Jastrow and a general broken-symmetry mean field reference. Examples include Jastrow antisymmetrized geminal power (JAGP), Jastrow-Pfaffians, and resonating valence bond (RVB) states among others, all of which can be treated with our algorithm. We will demonstrate using benchmark systems including the nitrogen molecule, a chain of hydrogen atoms, and the 2-D Hubbard model that a significant amount of correlation can be obtained by optimizing the energy of the SJMF wavefunction. This can be achieved at a relatively small cost when multiple symmetries including spin, particle number, and complex conjugation are simultaneously broken and projected. We also show that reduced density matrices can be calculated using the optimized wavefunctions, which allows us to calculate other observables such as correlation functions and will enable us to embed the VMC algorithm in a complete active space self-consistent field (CASSCF) calculation.