Enhancing Neural-Network Variational Monte Carlo through Basis Transformation

TL;DR

This paper introduces a physically motivated basis transformation for neural-network variational Monte Carlo that improves accuracy by making the ground state easier to represent without increasing neural network complexity.

Contribution

It proposes a basis transformation method that enhances variational expressivity in NNVMC with minimal computational overhead, applicable to existing neural-network architectures.

Findings

Lowered variational energy in benchmark tests.

Enabled more precise phase transition determination.

Applicable to multiple neural-network architectures.

Abstract

Neural-network variational Monte Carlo (NNVMC) has emerged as a powerful tool for solving quantum many-body problems, yet systematic pathways for improving its accuracy remain largely heuristic. Here, we introduce a physically motivated basis transformation for NNVMC that enhances variational expressivity without increasing the complexity of the neural-network ansatz itself. By formulating the many-body wave function in a Gaussian basis, we introduce a single learnable locality parameter, $\alpha$, that reshapes the target ground state into a more learnable representation. This approach introduces minimal computational overhead and can be readily combined with existing neural-network architectures. Using the three-dimensional homogeneous electron gas as a benchmark, we show that the optimized basis transformation consistently lowers the variational energy for both FermiNet and message-passing neural-network architectures. Notably, for the latter, it enables a more precise determination of the Fermi liquid to Wigner crystal phase transition. More broadly, our results highlight basis transformation as a new route to improving NNVMC in continuous space, showing that accuracy can be enhanced not only by refining the ansatz but also by making the target ground state easier to represent.