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

Eoghan Cronin1,*, Rajarshi Tiwari1,2,†, and Stefano Sanvito1,‡

  • *Contact author: eoghanc@tcd.ie
  • †Contact author: rajarshi.tiwari@ichec.ie
  • ‡Contact author: sanvitos@tcd.ie
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Phys. Rev. B 112, 195103 – Published 3 November, 2025

DOI: https://doi.org/10.1103/vm99-khkz

Abstract

The Hubbard model provides a test bed to investigate the complex behavior 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 lattice model, by minimizing an energy functional of the on-site occupations. The energy then comprises a contribution that depends on the external potential and a universal contribution describing the kinetic and the electron-electron interaction energy. Here we use machine learning to construct a class of scalable “semilocal” exchange-correlation functionals with an arbitrary degree of nonlocality 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. This effectively forms a close workflow for machine-learning Kohn-Sham lattice DFT. After having investigated how the accuracy of the semilocal approximation depends on the degree of nonlocality, we use our Kohn-Sham scheme to compute the polarizability of linear chains, either homogeneous or disordered, approaching the thermodynamic limit.

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Phys. Rev. B 112, 195103– Published 3 November, 2025
  • Received 27 January 2025
  • Revised 26 September 2025
  • Accepted 2 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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