Pure density functional for strong correlations and the thermodynamic limit from machine learning

TL;DR

This paper introduces a machine learning-based density functional that accurately captures strong electron correlations in one-dimensional hydrogen chains, surpassing traditional DFT methods and applicable to the thermodynamic limit.

Contribution

The authors develop a machine-learned density functional that accurately models strong correlations and can be used directly without orbitals, achieving quantum chemical accuracy for large systems.

Findings

Achieves quantum chemical accuracy in hydrogen chains

Handles strong correlations without specific difficulties

Applicable to the thermodynamic limit

Abstract

We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned approximation to $F[n]$, the universal part of the electronic density functional, to within quantum chemical accuracy. Our calculation (a) bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals, (b) includes the strong correlation of highly-stretched bonds without any specific difficulty (unlike all standard DFT approximations) and (c) is so accurate that it can be used to find the energy in the thermodynamic limit to quantum chemical accuracy.