Stochastic many-body perturbation theory for electron correlation energies

Abstract

Treating electron correlation more accurately and efficiently is at the heart of the development of electronic structure methods. In the present work, we explore the use of stochastic approaches to evaluate high-order electron correlation energies, whose conventional computational scaling is unpleasantly steep, being $O(N^{n+3})$ with respect to the system size $N$ and the perturbation order $n$ for the Møller-Plesset (MP) series. To this end, starting from Goldstone's time-dependent formulation of \emph{ab initio} many-body perturbation theory (MBPT), we present a reformulation of MBPT, which naturally leads to an Monte Carlo scheme with $O(n{N}^2+n^{2}N+f(n))$ scaling at each step, where $f(n)$ is a function of $n$ depending on the specific numerical scheme. Proof-of-concept calculations demonstrate that the proposed quantum Monte Carlo algorithm successfully extends the previous Monte Carlo approaches for MP2 and MP3 to higher orders. Therefore, for the first time the Goldstone's time-dependent formulation is made useful numerically for electron correlation energies, not only being purely as a theoretical tool.

arXiv comment8 pages, 3 figures

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Cited by in corpus (5)

• Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them
• Diagrammatic Monte Carlo Method for Impurity Models with General Interactions and Hybridizations
• Generalized many-body perturbation theory for the electron correlation energy: multi-reference random phase approximation via diagrammatic resummation
• Diagrammatic Monte Carlo for electronic correlation in molecules: high-order many-body perturbation theory with low scaling
• Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method