Auxiliary-field quantum Monte Carlo calculations for periodic solids with Brillouin zone sampling

Modern electronic structure methods are reaching a level of accuracy and efficiency, that enables simulation and prediction of important phenomena in solid-state chemistry. In order to allow for direct comparison with experiments, result of these simulations have to reach the thermodynamic limit of infinite system size, which substantially increases the cost of many-electron wave-function theories.
We derive and implement a technique to perform auxiliary-field quantum Monte Carlo (AFQMC) calculations [1] on realistic systems in arbitrary basis sets, accounting for symmetries of the Hamiltonian. Focussing on the case of Abelian symmetry groups, which includes translations in crystalline solids, weshow that accounting for symmetries reduces the cost of AFQMC by up to a factor N_k^-1, where N_k is the number of symmetry group elements.
The formalism is applied to crystalline solids, where accounting for symmetries enables more efficient extrapolations to the thermodynamic limit by Brillouin zone sampling [2]. Results for energetic and structural properties of semiconductors like diamond and hexagonal boron nitride are presented.

[1] M. Motta and S. Zhang, WIREs Comput Mol Sci, 8:e1364 (2018)
[2] J. McClain et al, J. Chem. Theory Comput. 13, 1209-1218 (2017)