Neural network-based nodal structures optimization for interacting fermionic systems

TL;DR

This paper introduces a neural network-based variational Monte Carlo method that adaptively optimizes nodal structures, achieving more accurate ground-state energies for strongly correlated fermionic systems like quantum dots.

Contribution

It presents a novel neural network ansatz that learns and optimizes fermionic wavefunction nodes during energy minimization, surpassing traditional methods in accuracy.

Findings

Achieves lower variational energies than fixed-node DMC.

Effectively learns and optimizes nodal structures.

Provides detailed insights into fermionic wavefunction properties.

Abstract

Simulating strongly correlated fermionic systems remains a fundamental challenge in quantum physics, largely due to the sign problem in quantum Monte Carlo (QMC) methods. We present a neural network-based variational Monte Carlo (NN-VMC) approach, leveraging a flexible neural network ansatz to represent the many-body wavefunction. Focusing on quantum dots with up to 30 electrons, we demonstrate that NN-VMC significantly reduces variational bias and achieves ground-state energies surpassing those of fixed-node diffusion Monte Carlo (DMC). A key feature is that the neural network adaptively learns and optimizes nodal structures during energy minimization. We provide qualitative insights into the nodal structure of fermionic wavefunctions by comparing the nodal structures generated by NN-VMC with those obtained from traditional trial functions. Additionally, we reveal spin-resolved radial distributions and electron density profiles, highlighting the versatility and accuracy of NN-VMC. This work underscores the potential of machine learning to advance quantum simulations and deepen our understanding of strongly correlated systems.