Size-consistent variational approaches to non-local pseudopotentials: standard and lattice regularized diffusion Monte Carlo methods revisited

TL;DR

This paper introduces improved, size-consistent variational algorithms for non-local pseudopotentials in diffusion Monte Carlo methods, enhancing accuracy and efficiency for large systems.

Contribution

It presents two upgraded algorithms for DMC and LRDMC that ensure size consistency and variational properties, with improved efficiency and error control.

Findings

Enhanced DMC scheme maintains effectiveness at small time-steps.

New LRDMC effective Hamiltonian reduces lattice-space error.

Introduced a randomization method requiring only a single lattice-space.

Abstract

We propose improved versions of the standard diffusion Monte Carlo (DMC) and the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC method, we refine a scheme recently devised to treat non-local pseudopotential in a variational way. We show that such scheme --when applied to large enough systems-- maintains its effectiveness only at correspondingly small enough time-steps, and we present two simple upgrades of the method which guarantee the variational property in a size-consistent manner. For the LRDMC method, which is size-consistent and variational by construction, we enhance the computational efficiency by introducing (i) an improved definition of the effective lattice Hamiltonian which remains size-consistent and entails a small lattice-space error with a known leading term, and (ii) a new randomization method for the positions of the lattice knots which requires a single lattice-space.