Neural Network Solutions of Bosonic Quantum Systems in One Dimension

TL;DR

This paper demonstrates the effectiveness of neural networks in solving one-dimensional bosonic quantum systems, benchmarking their accuracy against exact solutions and introducing symmetric inputs to handle particle exchange symmetries.

Contribution

It introduces a neural network approach for bosonic quantum systems, including symmetric input handling, and benchmarks scalability with multiple particles against exact solutions.

Findings

Neural networks accurately approximate ground states of 1D bosonic systems.

Symmetric input functions effectively enforce particle exchange symmetry.

Method scales well with increasing particle number.

Abstract

Neural networks have been proposed as efficient numerical wavefunction ansatze which can be used to variationally search a wide range of functional forms for ground state solutions. These neural network methods are also advantageous in that more variational parameters and system degrees of freedom can be easily added. We benchmark the methodology by using neural networks to study several different integrable bosonic quantum systems in one dimension and compare our results to the exact solutions. While testing the scalability of the procedure to systems with many particles, we also introduce using symmetric function inputs to the neural network to enforce exchange symmetries of indistinguishable particles.