Self-Healing Diffusion Monte Carlo Correction of Sign Errors in Periodic Solids

Diffusion Monte Carlo (DMC) scales with electron count as (N³-N⁴) which makes it appealing for solid-state systems. Practical applications of DMC often rely on the fixed-node approximation to avoid the fermion sign problem. This introduces a bias, which is one of the sources of errors in DMC calculations in real materials, denoted as nodal errors. Frequently, these nodal errors arise due to the use of approximate nodes of trial wavefunctions often obtained with mean-field methods. In this talk, we present results that demonstrate that Self-Healing Diffusion Quantum Monte Carlo (SHDMC) is capable of strongly reducing the nodal error and can be applied to obtain a very compact, but high-quality wavefunction for solids. Although SHDMC can be applied in larger systems, we use a single unit cell of graphene as a test case because this allows us to benchmark SHDMC results against selected CI results obtained using correlation consistent bases of increasing size. We find that SHDMC reduces the fixed node error exponentially with respect to sampling effort, independent of the initial conditions. We further compare the total energies of graphene obtained from SHDMC with basis set extrapolated selected CI and analyze the compactness of the resulting multireference wavefunctions. We will discuss potential future applications of SHDMC in predicting the properties of strongly correlated and other complex materials.