Neural-Network Quantum States for Periodic Systems in Continuous Space

TL;DR

This paper presents a novel neural quantum state framework using Deep Sets for simulating strongly interacting periodic systems in continuous space, achieving high accuracy in energy and distribution estimations.

Contribution

It introduces a permutationally-invariant neural network approach tailored for periodic quantum systems, extending neural quantum states to continuous and periodic domains.

Findings

Accurate ground-state energy estimations for 1D and 2D systems.

Effective description of periodic bosonic systems with neural networks.

Comparable results to traditional methods in 2D systems.

Abstract

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in terms of a permutationally-invariant part described by the Deep Sets neural-network architecture. The input coordinates to the Deep Sets are periodically transformed such that they are suitable to directly describe periodic bosonic systems. We show example applications to both one and two-dimensional interacting quantum gases with Gaussian interactions, as well as to $^4$He confined in a one-dimensional geometry. For the one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.