Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo

TL;DR

This paper introduces an efficient method for sampling unbiased reduced density matrices in Full Configuration Interaction Quantum Monte Carlo, enabling accurate computation of electronic properties with minimal additional computational cost.

Contribution

It presents a novel approach using independent replica populations to obtain unbiased reduced density matrices in FCIQMC, improving property calculations.

Findings

Unbiased reduced density matrices can be sampled with small overheads.

The method yields rapid convergence to exact properties.

A quasi-variational energy estimate offers an accurate alternative to traditional estimators.

Abstract

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the Full Configuration Interaction Quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself), and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.