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

Di Luo and Bryan K. Clark
Phys. Rev. Lett. 122, 226401 – Published 4 June 2019
PDFHTMLExport Citation

Abstract

Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this Letter, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman and Cohen [Phys. Rev. 102, 1189 (1956)], 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 learn the optimal transformation via variational Monte Carlo calculations. 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 [L. F. Tocchio et al., Phys. Rev. B 78, 041101(R) (2008)], which we show how to explicitly represent as a NNB. We benchmark the NNB on Hubbard models 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 25 August 2018
  • Revised 12 January 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.226401

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Di Luo and Bryan K. Clark

  • Institute for Condensed Matter Theory and Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 122, Iss. 22 — 7 June 2019

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×