Machine Learning Universal Bosonic Functionals
- URL: http://arxiv.org/abs/2104.03208v3
- Date: Wed, 25 Aug 2021 09:41:33 GMT
- Title: Machine Learning Universal Bosonic Functionals
- Authors: Jonathan Schmidt, Matteo Fadel, and Carlos L. Benavides-Riveros
- Abstract summary: A functional theory for bosonic ground states establishes the existence of a universal functional $mathcalF[gamma]$ that recovers quantum correlations exactly.
For the Bose-Hubbard model, we present a comparison between our approach and Quantum Monte Carlo.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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