Improved Lieb–Oxford bound on the indirect and exchange energies

article Improved Lieb–Oxford bound on the indirect and exchange energies published yes Mathieu Lewin author Elliott H. Lieb author Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department Analysis of quantum many-body systems project 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. Springer Nature2022 eng Mathematical PhysicsStatistical and Nonlinear Physics Letters in Mathematical Physics 0377-9017 1573-0530 2203.12473 00085476260000110.1007/s11005-022-01584-5 1125 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:<a href="https://doi.org/10.1007/s11005-022-01584-5">10.1007/s11005-022-01584-5</a>. Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. Springer Nature. <a href="https://doi.org/10.1007/s11005-022-01584-5">https://doi.org/10.1007/s11005-022-01584-5</a> 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 M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:<a href="https://doi.org/10.1007/s11005-022-01584-5">10.1007/s11005-022-01584-5</a> M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022). 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. <a href="https://doi.org/10.1007/s11005-022-01584-5">https://doi.org/10.1007/s11005-022-01584-5</a>. 122462023-01-16T09:53:54Z2025-04-14T07:26:59Z