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Description
An accurate numerical method is presented for computing the ground state of a many-electron system in the low-density limit first considered by Seidl (Phys. Rev. A 1999). In this limit the ground state problem reduces to a multi-marginal optimal transport (MMOT) problem. The method is an improved version of the Genetic Column Generation algorithm by Friesecke, Schulz and Voegler introduced in SIAM J. Sci. Comput. 44 (2022). Via a more global search rule it allows to find the ground state of MMOT problems with ~ 10⁶⁰ degrees of freedom to machine precision. Applying the method to the uniform electron gas in two dimensions confirms the effect of Wigner crystallization, that is, formation of a periodic lattice of electrons. Joint work with A.Parmiggiani, M.Penka, A.S.Schulz.
