Alleviation of the Fermion-sign problem by optimization of many-body wave functions

TL;DR

This paper introduces an efficient optimization method for many-body wave functions in quantum Monte Carlo calculations, significantly reducing the fermion-sign problem and improving accuracy in molecular energy predictions.

Contribution

The authors develop a robust diagonalization-based optimization technique that systematically minimizes fixed-node errors in quantum Monte Carlo simulations.

Findings

Achieved experimental accuracy of 0.02 eV for C₂ molecule binding energy.

Demonstrated systematic reduction of fixed-node errors.

Applicable to both continuum systems and lattice models.

Abstract

We present a simple, robust and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice models. Based on a strong zero-variance principle, diagonalization of the Hamiltonian matrix in the space spanned by the wav e function and its derivatives determines the optimal parameters. It systematically reduces the fixed-node error, as demonstrated by the calculation of the binding energy of the small but challenging C$_2$ molecule to the experimental accuracy of 0.02 eV.