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

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.

13 pages, 5 figures, To be published in Journal of Chemical Physics (Accepted)

References in corpus (4)

• Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer
• The sign problem in full configuration interaction quantum Monte Carlo: Linear and sub-linear representation regimes for the exact wave function
• The effect of quantization on the FCIQMC sign problem
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Cited by in corpus (12)

• NECI: N-Electron Configuration Interaction with emphasis on state-of-the-art stochastic methods
• Unbiasing the initiator approximation in Full Configuration Interaction Quantum Monte Carlo
• Stochastic multi-reference perturbation theory with application to linearized coupled cluster method
• Efficient and Stochastic Multireference Perturbation Theory for Large Active Spaces within a Full Configuration Interaction Quantum Monte Carlo Framework
• Combined unitary and symmetric group approach applied to low-dimensional spin systems
• Photoemission Spectra from Reduced Density Matrices: the Band Gap in Strongly Correlated Systems
• Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo
• Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions
• Diagrammatic Coupled Cluster Monte Carlo
• Improved Stochastic Multireference Perturbation Theory for Correlated Systems with Large Active Spaces
• Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity
• Spin-pure Stochastic-CASSCF via GUGA-FCIQMC applied to Iron Sulfur Clusters