Taming the expressiveness of neural-network wave functions for robust convergence to quantum many-body states

TL;DR

This paper introduces a variance-based loss function for neural-network quantum states, significantly improving convergence and enabling systematic energy spectrum estimation in many-body fermionic systems.

Contribution

It proposes a novel variance minimization approach that enhances neural network training for quantum states and allows spectrum extraction.

Findings

Variance minimization improves convergence speed.

Method effectively estimates energy spectra across multiple runs.

Demonstrated on 2D spin systems with attractive interactions.

Abstract

Neural networks are emerging as a powerful tool for determining the quantum states of interacting many-body fermionic systems. The standard approach trains a neural-network ansatz by minimizing the mean local energy estimated from Monte Carlo samples. However, this typically results in large sample-to-sample fluctuations in the estimated mean energy and thus slow convergence of the energy minimization. We propose that minimizing a logarithmically compressed variance of the local energies can dramatically improve convergence. Moreover, this loss function can be adapted to systematically obtain the energy spectrum across multiple runs. We demonstrate these ideas for spin-1/2 particles in a 2D harmonic trap with attractive Poschl-Teller interactions between opposite spins.