Mitigating the Hubbard sign problem with complex-valued neural networks

Marcel Rodekamp, Evan Berkowitz, Christoph Gäntgen, Stefan Krieg, Thomas Luu, and Johann Ostmeyer
Phys. Rev. B 106, 125139 – Published 22 September 2022

Abstract

Monte Carlo simulations away from half filling suffer from a sign problem that can be reduced by deforming the contour of integration. Such a transformation, which induces a Jacobian determinant in the Boltzmann weight, can be implemented using neural networks. This additional determinant cost for a generic neural network scales cubically with the volume, preventing large-scale simulations. We implement an architecture, based on complex-valued affine coupling layers, which reduces this to linear scaling. We demonstrate the efficacy of this method by successfully applying it to systems of different size, the largest of which is intractable by other Monte Carlo methods due to its severe sign problem.

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  • Received 21 March 2022
  • Revised 26 August 2022
  • Accepted 2 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.125139

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Marcel Rodekamp1,2,3,4, Evan Berkowitz1,2,3, Christoph Gäntgen1,3,4, Stefan Krieg1,2,3,4, Thomas Luu1,4,5, and Johann Ostmeyer6

  • 1Institute for Advanced Simulation, Forschungszentrum Jülich, 54245 Jülich, Germany
  • 2JARA & Jülich Supercomputing Center, Forschungszentrum Jülich, 54245 Jülich, Germany
  • 3Center for Advanced Simulation and Analytics (CASA), Forschungszentrum Jülich, 52425 Jülich, Germany
  • 4Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, 53115 Bonn, Germany
  • 5Institut für Kernphysik, Forschungszentrum Jülich, 54245 Jülich, Germany
  • 6Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom

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Issue

Vol. 106, Iss. 12 — 15 September 2022

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