Improved Lieb–Oxford bound on the indirect and exchange energies
Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 112(5), 92.
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Author
Lewin, Mathieu;
Lieb, Elliott H.;
Seiringer, RobertISTA 
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Abstract
The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of a classical system of N identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree–Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy.
Publishing Year
Date Published
2022-09-15
Journal Title
Letters in Mathematical Physics
Acknowledgement
We would like to thank David Gontier for useful advice on the numerical simulations. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful for the hospitality of the Institut Henri Poincaré in Paris, where part of this work was done.
Volume
112
Issue
5
Article Number
92
ISSN
eISSN
IST-REx-ID
Cite this
Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:10.1007/s11005-022-01584-5
Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-022-01584-5
Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-022-01584-5.
M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the indirect and exchange energies,” Letters in Mathematical Physics, vol. 112, no. 5. Springer Nature, 2022.
Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 112(5), 92.
Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics, vol. 112, no. 5, 92, Springer Nature, 2022, doi:10.1007/s11005-022-01584-5.
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