{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/machine-learning-semi-local-exchange","title":"Machine-learning semi-local exchange-correlation functionals for Kohn-Sham density functional theory of the Hubbard model","arxiv_id":"2501.16893","date":"2025-01-28","proceeding":null,"authors":["Eoghan Cronin","Rajarshi Tiwari","Stefano Sanvito"],"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.","url_abs":"https://arxiv.org/abs/2501.16893v1","url_pdf":"https://arxiv.org/pdf/2501.16893v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"machine-learning-semi-local-exchange","repo_url":"https://github.com/eoghancronin/ml-ldft","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}