Machine Learning Universal Bosonic Functionals

TL;DR

This paper introduces a machine learning approach to approximate the universal bosonic functional in reduced density matrix functional theory, enabling efficient computation and comparison with Quantum Monte Carlo for bosonic systems.

Contribution

It develops a novel method to design reliable approximations for the universal functional using a new decomposition of the density matrix and machine learning techniques.

Findings

Efficient computation of the universal functional for bosonic systems.

Comparison shows competitive accuracy with Quantum Monte Carlo.

Simplification of the functional search process for translational invariant systems.

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.