Benchmarking Density Functional Theory with Density Matrix Renormalization Group and Lessons For Higher Dimensions*

Kohn-Sham Density Functional Theory (DFT) is a mathematically exact method that requires approximation to the exchange correlation energy which may exclude features seen in experiment or provide inadequate estimates. Meanwhile, we may use Density Matrix Renormalization Group (DMRG), a numerical method which can accurately treat strongly correlated electrons in one dimension, to find exact DFT quantities such as the Kohn-Sham potential [1]. We use DMRG in one dimension as a benchmark to test new functionals. Further, recommendations for calculations in two and three dimensional systems are discussed as well as computational proof of principles [2]. [1] E.M. Stoudenmire, et.~al., {\it Phys.~Rev.~Lett.} {\bf 109}, 056402 (2012) [2] Lucas O. Wagner, et.~al., {\it Phys.~Rev.~Lett.} {\bf 111}, 093003 (2013)