Symmetry enforced solution of the many-body Schr\"odinger equation with deep neural network

TL;DR

This paper introduces a neural network-enhanced Variational Monte Carlo method that enforces spin symmetry, enabling accurate and efficient calculation of ground and excited states in strongly correlated quantum systems.

Contribution

It presents a novel approach to incorporate spin symmetry into neural network-based VMC, improving accuracy and computational efficiency for quantum state calculations.

Findings

Accurately predicts energies of quantum states with specific spin symmetry.

Effectively computes spin gaps, including singlet-triplet gaps in biradicals.

Maintains correct symmetry in strongly correlated systems.

Abstract

The integration of deep neural networks with the Variational Monte Carlo (VMC) method has marked a significant advancement in solving the Schr\"odinger equation. In this work, we enforce spin symmetry in the neural network-based VMC calculation with modified optimization target. Our method is designed to solve for the ground state and multiple excited states with target spin symmetry at a low computational cost. It predicts accurate energies while maintaining the correct symmetry in strongly correlated systems, even in cases where different spin states are nearly degenerate. Our approach also excels at spin-gap calculations, including the singlet-triplet gap in biradical systems, which is of high interest in photochemistry. Overall, this work establishes a robust framework for efficiently calculating various quantum states with specific spin symmetry in correlated systems, paving the way for novel discoveries in quantum science.