Permutation invariant multi-scale full quantum neural network wavefunction

TL;DR

This paper introduces a neural network framework capable of modeling the full quantum wavefunction of complex many-body systems, including electrons, nuclei, and muons, capturing quantum effects beyond traditional approximations.

Contribution

It presents a permutation-invariant, multi-scale neural network approach that models full quantum wavefunctions without relying on the Born-Oppenheimer approximation.

Findings

Successfully validated on molecular systems

Captures nuclear quantum effects and particle couplings

Provides a computationally feasible modeling method

Abstract

Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural network framework that overcomes this barrier by modeling the full quantum wavefunction of a system, including electrons, nuclei and muons, directly capturing the full quantum effects beyond the Born-Oppenheimer approximation. The neural network approximates joint wavefunction of different interacting particles with a rigorous handling of permutation invariance, enabling simultaneous treatment of nuclear quantum effects and electron-nucleus-muon couplings without explicit excited states. Validated on molecular systems, this approach offers a computationally feasible way to model full quantum phenomena in complex many-body systems, establishing a direct connection between fundamental particle properties and emergent material behavior.