Electronic structure quantum Monte Carlo

TL;DR

Quantum Monte Carlo (QMC) is a powerful and accurate computational method for studying electronic structures in many-body quantum systems, with recent advances addressing the fermion sign problem and improving predictive accuracy.

Contribution

This review highlights recent progress in electronic structure QMC, including analysis of fermion nodes, development of Pfaffian wave functions, and the introduction of backflow coordinates.

Findings

QMC achieves 90-95% of correlation energy in real systems.

Analysis of fermion nodes reveals minimal nodal domains in ground states.

Pfaffian wave functions and backflow coordinates improve accuracy and reduce fixed-node bias.

Abstract

Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion Hamiltonians. Some of the key QMC achievements include direct treatment of electron correlation, accuracy in predicting energy differences and favorable scaling in the system size. Calculations of atoms, molecules, clusters and solids have demonstrated QMC applicability to real systems with hundreds of electrons while providing 90-95% of the correlation energy and energy differences typically within a few percent of experiments. Advances in accuracy beyond these limits are hampered by the so-called fixed-node approximation which is used to circumvent the notorious fermion sign problem. Many-body nodes of fermion states and their properties have therefore become one of the important topics for further progress in predictive power and efficiency of QMC calculations. Some of our recent results on the wave function nodes and related nodal domain topologies will be briefly reviewed. This includes analysis of few-electron systems and descriptions of exact and approximate nodes using transformations and projections of the highly-dimensional nodal hypersurfaces into the 3D space. Studies of fermion nodes offer new insights into topological properties of eigenstates such as explicit demonstrations that generic fermionic ground states exhibit the minimal number of two nodal domains. Recently proposed trial wave functions based on Pfaffians with pairing orbitals are presented and their nodal properties are tested in calculations of first row atoms and molecules. Finally, backflow "dressed" coordinates are introduced as another possibility for capturing correlation effects and for decreasing the fixed-node bias.