Machine-learning semi-local exchange-correlation functionals for Kohn-Sham density functional theory of the Hubbard model

TL;DR

This paper develops machine learning-based semi-local exchange-correlation functionals for lattice DFT of the Hubbard model, enabling accurate Kohn-Sham calculations and properties prediction for strongly correlated systems.

Contribution

It introduces a scalable machine learning approach to construct semi-local functionals with tunable non-locality for the Hubbard model, advancing lattice DFT methods.

Findings

The accuracy improves with increased non-locality in the functional.

The Kohn-Sham scheme accurately predicts polarizability of linear chains.

The method approaches the thermodynamic limit for disordered systems.

Abstract

The Hubbard model provides a test bed to investigate the complex behaviour arising from electron-electron interaction in strongly-correlated systems and naturally emerges as the foundation model for lattice density functional theory (DFT). Similarly to conventional DFT, lattice DFT computes the ground-state energy of a given Hubbard model, by minimising a universal energy functional of the on-site occupations. Here we use machine learning to construct a class of scalable `semi-local' exchange-correlation functionals with an arbitrary degree of non-locality for the one-dimensional spinfull Hubbard model. Then, by functional derivative we construct an associated Kohn-Sham potential, that is used to solve the associated Kohn-Sham equations. After having investigated how the accuracy of the semi-local approximation depends on the degree of non-locality, we use our Kohn-Sham scheme to compute the polarizability of linear chains, either homogeneous or disordered, approaching the thermodynamic limit. approaching the thermodynamic limit.