Comparison of systematically improvable DMC and AFQMC for condensed matter*

Diffusion Monte Carlo (DMC) and Auxiliary Field Quantum Monte Carlo (AFQMC) can both have their approximations systematically improved by applying successively more accurate trial wavefunctions. In this work we assess the cost and feasibility of determining exact total energies for solid state Hamiltonians by studying primitive cells of four representative materials, Al, LiF, C and TiO2. Specifically, we utilize multideterminant trial wavefunctions generated via selective CI techniques with various sizes of single particle basis. Attention is paid to the rate at which the error decreases as the trial wavefunction includes more determinants and also to the cost as the basis increases in size. In this way, we are able to compare both DMC and AFQMC on equal terms at identical levels of approximation.