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

We describe how to incorporate symmetries of the Hamiltonian into auxiliary-field quantum Monte Carlo (AFQMC) calculations. Focusing on the case of Abelian symmetries, we show that the computational cost of most steps of an AFQMC calculation is reduced by N^(-1)_k, 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.