Density functional theory (DFT) is based on the proven idea that the energy of a system can be found simply from the electronic density of that system, and the successful implementation of DFT via the Kohn-Sham (KS) equations has proven the practicality of this idea.  To understand density functional approximations and how to make them better, it is vital that we look at the exact density functional.  The exact functional, however, is extremely costly to implement, because it requires a way to solve for the true ground state energy and density of the interacting electron system.  Density matrix renormalization group (DMRG) provides such a wavefunction solver and is highly efficient in one dimension.  Using DMRG, we implement exact density functional for some 1d systems modeling the continuum with a long-range soft-Coulomb interaction.  Results for some atom chains are discussed and compared to LDA calculations.

Exact density functional theory with the density matrix renormalization group

243rd National Meeting (2012)

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