Multireference diffusion Monte Carlo reaches 2D materials

Abstract

The advantageous scaling of DMC with electron count ($N^3-N^4$) makes it an appealing choice for many-body calculations of solid-state systems. One of the sources of errors in diffusion Monte Carlo (DMC) calculations in real materials is the nodal error, which arises from using approximate nodes of trial wavefunctions often obtained with mean-field methods. In this work we show that Self-Healing Diffusion Quantum Monte Carlo (SHDMC) can be applied to obtain a very compact, but high-quality wavefunction for solids using a single unit cell of graphene as a test case. Although SHDMC can be applied in larger systems, performing SHDMC on a single unit cell allows us to benchmark SHDMC results against selected CI results using correlation consistent bases of increasing size. We find that SHDMC reduces the fixed node error exponentially versus 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. Our work paves the way for future applications of SHDMC in predicting the properties of more strongly correlated and other complex materials.