# Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure

## TL;DR

This paper introduces a method to incorporate Hamiltonian symmetries into auxiliary-field quantum Monte Carlo calculations, significantly reducing computational costs especially for crystalline solids with many k points.

## Contribution

The authors develop a formalism to include Abelian symmetries in AFQMC, leading to computational cost reductions and enabling more efficient simulations of large systems.

## Key findings

- Cost reduction by factor of N_k^{-1} in AFQMC steps
- Effective for molecular and crystalline systems
- Enables calculations approaching the thermodynamic limit

## Abstract

We describe how to incorporate symmetries of the Hamiltonian into auxiliary-field quantum Monte Carlo calculations (AFQMC). Focusing on the case of Abelian symmetries, we show that the computational cost of most steps of an AFQMC calculation is reduced by $N_k^{-1}$, where $N_k$ is the number of irreducible representations of the symmetry group. We apply the formalism to a molecular system as well as to several crystalline solids. In the latter case, the lattice translational group provides increasing savings as the number of k points is increased, which is important in enabling calculations that approach the thermodynamic limit. The extension to non-Abelian symmetries is briefly discussed.