Erlangen 2022 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 19: Ultra-cold atoms, ions and BEC I (joint session A/Q)
Q 19.5: Talk
Tuesday, March 15, 2022, 11:30–11:45, A-H2
Machine learning universal bosonic functionals — •Benavides-Riveros Carlos L.1, Schmidt Jonathan2, and Fadel Matteo3 — 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany — 2Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany — 3Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
The one-body reduced density matrix γ plays a fundamental role in describing and predicting quantum features of bosonic systems, ultra-cold gases or Bose-Einstein condensates. 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 novel decomposition of γ, we have developed a method to design reliable approximations for such universal functionals [1]. Our results demonstrate 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.
[1] Phys. Rev. Research 3, L032063 (2021).