Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions

TL;DR

This paper introduces neural network backflow (NNB), a novel wave function ansatz for quantum many-body problems that enhances accuracy by transforming single-particle orbitals with neural networks, improving upon traditional backflow methods.

Contribution

The paper presents a new neural network-based backflow wave function that generalizes and improves traditional backflow approaches for quantum many-body systems.

Findings

NNB significantly reduces the relative error in Hubbard model simulations.

It restores symmetry in observables and orbitals.

It decreases double-occupancy density.

Abstract

Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this paper, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman, adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to find the optimal transformation. NNB directly dresses a mean-field state, can be systematically improved and directly alters the sign structure of the wave-function. It generalizes the standard backflow which we show how to explicitly represent as a NNB. We benchmark the NNB on a Hubbard model at intermediate doping finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.