Machine-learning semi-local exchange-correlation functionals for Kohn-Sham density functional theory of the Hubbard model
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| Format: | Preprint |
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2025
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| _version_ | 1866916586751787008 |
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| author | Cronin, Eoghan Tiwari, Rajarshi Sanvito, Stefano |
| author_facet | Cronin, Eoghan Tiwari, Rajarshi Sanvito, Stefano |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_16893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Machine-learning semi-local exchange-correlation functionals for Kohn-Sham density functional theory of the Hubbard model Cronin, Eoghan Tiwari, Rajarshi Sanvito, Stefano Strongly Correlated Electrons 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. |
| title | Machine-learning semi-local exchange-correlation functionals for Kohn-Sham density functional theory of the Hubbard model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2501.16893 |