Approximating Excited States using Neural Networks

TL;DR

This paper introduces a neural network approach to approximate excited quantum states by training with a variational principle and orthogonality penalties, demonstrating effectiveness on harmonic oscillators.

Contribution

It extends neural network wave function methods to excited states using orthogonality constraints, a novel approach in this domain.

Findings

Successful computation of excited states for harmonic oscillators

Neural network method achieves accurate results

Demonstrates potential for complex quantum systems

Abstract

Recently developed neural network-based wave function methods are capable of achieving state-of-the-art results for finding the ground state in real space. In this work, a neural network-based method is used to compute excited states. We train our network via variational principle, along a further penalty term that imposes the orthogonality with lower-energy eigenfunctions. As a demonstration of the effectiveness of this approach, results from numerical calculations for one-dimensional and two-dimensional harmonic oscillators are presented.