Diagrammatic Monte Carlo for electronic correlation in molecules: high-order many-body perturbation theory with low scaling

TL;DR

This paper introduces a low-scaling diagrammatic Monte Carlo method that efficiently computes high-order molecular correlation energies using combinatorial graph theory, significantly reducing computational complexity.

Contribution

It develops a novel stochastic approach that encodes many-body diagrams with graph theory, enabling accurate correlation energy calculations up to MP5 with quadratic basis scaling.

Findings

Achieved accurate MP5 correlation energies

Reduced computational complexity to quadratic scaling

Enabled stochastic calculations for complex many-body systems

Abstract

We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the M{\o}ller-Plesset (MPn) perturbation series, obtaining accurate correlation energies up to n = 5, with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecular many-fermion correlation problem, opening up the possibility of low-scaling, accurate stochastic computations for a wide class of many-body systems described by Hugenholtz diagrams.