Size Extensive Auxiliary-Field Quantum Monte Carlo with Perturbative Coupled Cluster Trial Wavefunction

TL;DR

This paper introduces a size-extensive AFQMC method using perturbative CCSD trial wavefunctions, achieving high accuracy with reduced bias and improved scalability for large systems, including the uniform electron gas.

Contribution

The authors develop a novel size-extensive AFQMC approach with perturbative CCSD trials that scales efficiently and avoids divergence issues in the thermodynamic limit.

Findings

Achieves accuracy comparable to CISD trial wavefunctions for small systems.

Outperforms CCSD(T) in accuracy and noise levels.

Remains free of infrared divergence in the thermodynamic limit.

Abstract

In this work, we develop a size extensive Auxiliary-Field Quantum Monte Carlo (AFQMC) approach that scales as $O(N^5)$ for local energy evaluation by treating the Coupled Cluster Singles and Doubles (CCSD) trial wavefunctions perturbatively. Comprehensive numerical examinations, spanning from main-group molecules to $3d$ transition metal complexes, demonstrate that this perturbative treatment introduces negligible bias. For small systems, our method achieves an accuracy and level of noise comparable to AFQMC with configuration interaction singles and doubles (CISD) trial wavefunctions while outperforming CCSD(T). This size extensivity offers a decisive advantage for large systems, as suggested by the ground state energies of non-interacting monomers and one-dimensional atomic chains. Finally, the numerical simulations of the uniform electron gas (UEG) provide evidence that, unlike the CCSD(T) method, our new approach does not suffer from infrared divergence in the thermodynamic limit (TDL).