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  • Letter
  • Open Access

Machine learning universal bosonic functionals

Jonathan Schmidt1, Matteo Fadel2, and Carlos L. Benavides-Riveros3,4,*

  • 1Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany
  • 2Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
  • 3Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
  • 4NR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, Via Salaria Km 29.3, I-00016 Monterotondo Scalo, Italy

  • *carlosbe@pks.mpg.de
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Phys. Rev. Research 3, L032063 – Published 13 September, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032063

Abstract

The one-body reduced density matrix γ plays a fundamental role in describing and predicting quantum features of bosonic systems, such as Bose-Einstein condensation. The recently proposed reduced density matrix functional theory for bosonic ground states establishes the existence of a universal functional F[γ] that recovers quantum correlations exactly. Based on a decomposition of γ, we have developed a method to design reliable approximations for such universal functionals: Our results suggest that for translational invariant systems the constrained search approach of functional theories can be transformed into an unconstrained problem through a parametrization of a Euclidian space. This simplification of the search approach allows us to use standard machine learning methods to perform a quite efficient computation of both F[γ] and its functional derivative. For the Bose-Hubbard model, we present a comparison between our approach and the quantum Monte Carlo method.

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Phys. Rev. Research 3, L032063– Published 13 September, 2021
  • Received 31 March 2021
  • Accepted 25 August 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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