Nonlinear Network description for many-body quantum systems in continuous space

TL;DR

This paper introduces a neural network-inspired wave function approach using iterative backflow renormalization, significantly improving accuracy in variational Monte Carlo simulations of liquid helium in various phases and dimensions.

Contribution

It interprets iterative backflow as a neural network, achieving higher accuracy in quantum many-body simulations and unifying liquid and solid phase descriptions with a single functional form.

Findings

Tenfold accuracy improvement over traditional wave functions for liquid helium

Close agreement of extrapolated energies with exact values

Unified description of liquid and solid phases in 2D helium

Abstract

We show that the recently introduced iterative backflow renormalization can be interpreted as a general neural network in continuum space with non-linear functions in the hidden units. We use this wave function within Variational Monte Carlo for liquid $^4$He in two and three dimensions, where we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation of these energies to zero variance gives values in close agreement with the exact values. For two dimensional $^4$He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form -a feature shared with the Shadow Wave Function, but now joined by much higher accuracy. We also achieve significant progress for liquid $^3$He in three dimensions, improving previous variational and fixed-node energies for this very challenging fermionic system.