Machine Learning Universal Bosonic Functionals

Abstract

The one-body reduced density matrix $\gamma$ 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 $\mathcal{F}[\gamma ]$ that recovers quantum correlations exactly. Based on a novel decomposition of $\gamma$, 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 an Euclidian space. This simplification of the search approach allows us to use standard machine-learning methods to perform a quite efficient computation of both $\mathcal{F}[\gamma ]$ and its functional derivative. For the Bose-Hubbard model, we present a comparison between our approach and Quantum Monte Carlo.

13 pages, 6 figures; close to the published version

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• Tools for quantum simulation with ultracold atoms in optical lattices
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• Solving the Bose-Hubbard model with machine learning
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Cited by in corpus (6)

• Machine learning the derivative discontinuity of density-functional theory
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Deriving density-matrix functionals for excited states
• Elucidating the molecular orbital dependence of the total electronic energy in multireference problems
• Density-matrix functional theory of the attractive Hubbard model: Statistical analogy of pairing correlations
• Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory