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Machine learning universal bosonic functionals

Authors: J. Schmidt, M. Fadel, and C.L. Benavides-Riveros

Ref.: Phys. Rev. Research 3, L032063 (2021)

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.

Citations: 3 (Google scholar)

DOI: 10.1103/PhysRevResearch.3.L032063

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Bibtex:

@article{Schmidt_2021,
	doi = {10.1103/physrevresearch.3.l032063},
	url = {https://doi.org/10.1103%2Fphysrevresearch.3.l032063},
	year = 2021,
	month = {sep},
	publisher = {American Physical Society ({APS})},
	volume = {3},
	number = {3},
	author = {Jonathan Schmidt and Matteo Fadel and Carlos L. Benavides-Riveros},
	title = {Machine learning universal bosonic functionals},
	journal = {Physical Review Research}
}