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arXiv · 2501.16893

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

Eoghan Cronin·Rajarshi Tiwari·Stefano Sanvito
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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.

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Eoghan Cronin, Rajarshi Tiwari, Stefano Sanvito. 2025-01-28. Machine-learning semi-local exchange-correlation functionals for Kohn-Sham density functional theory of the Hubbard model. https://arxiv.org/abs/2501.16893

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