Machine learning universal bosonic functionals

Jonathan Schmidt

doi:10.1103/PhysRevResearch.3.L032063

Machine learning universal bosonic functionals

2021-09-13

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AI

Carlos L. Benavides-Riveros *

DOI：10.1103/PhysRevResearch.3.L032063

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Abstract

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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 F[gamma] that recovers quantum correlations exactly. Based on a 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 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[gamma] and its functional derivative. For the Bose-Hubbard model, we present a comparison between our approach and the quantum Monte Carlo method.

Keywords:

REDUCED DENSITY-MATRIX

CORRELATION ENERGIES

ENTANGLEMENT

2-PARTICLE

ORBITALS

ATOMS

Machine learning universal bosonic functionals

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