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We describe how to incorporate symmetries of the Hamiltonian intoauxiliary-field quantum Monte Carlo calculations (AFQMC). Focusing on the caseof Abelian symmetries, we show that the computational cost of most steps of anAFQMC calculation is reduced by $N_k^{-1}$, where $N_k$ is the number ofirreducible representations of the symmetry group. We apply the formalism to amolecular system as well as to several crystalline solids. In the latter case,the lattice translational group provides increasing savings as the number of kpoints is increased, which is important in enabling calculations that approachthe thermodynamic limit. The extension to non-Abelian symmetries is brieflydiscussed.

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