Density Functional Theory Comparisons with
Density Matrix Renormalization Group

Density Functional Theory (DFT) is a computationally quick means of determining the electronic structure; however, it may miss key aspects of the system. Making sure that this method is accurately giving the correct electronic structure is of vital importance in the development of new materials. Meanwhile, Density Matrix Renormalization Group (DMRG) is a computationally inexpensive way to calculate the properties of one dimensional materials. By examining DFT methods and DMRG in one dimension, we can make recommendations on the use of DFT in two- and three-dimensions. The scope of this project covers all aspects of DFT.

We have demonstrated that DMRG is a suitable comparison in one dimension [Phys. Rev. Lett. 109, 056402 (2012)] and can solve systems with a large numbers of atoms. We also develop benchmarks for use in testing functionals on one dimensional systems to judge their accuracy on new functionals [Phys. Chem. Chem. Phys., 14, 8581-8590 (2012)]. We were also able to show that the Kohn-Sham algorithm converges absolutely in one dimension [Phys. Rev. Lett. 111,093003 (2013) ]

Publications
[176] Pure density functional for strong correlation and the thermodynamic limit from machine learning Li Li, Thomas E. Baker, Steven R. White, Kieron Burke, Phys. Rev. B 94, 245129 (2016). [bibtex] [pdf] [doi]
[164] One-dimensional mimicking of electronic structure: The case for exponentials Thomas E. Baker, E. Miles Stoudenmire, Lucas O. Wagner, Kieron Burke, Steven R. White, Phys. Rev. B 91, 235141 (2015). [data] [summary] [bibtex] [pdf] [doi]
[154] Kohn-Sham calculations with the exact functional Lucas O. Wagner, Thomas E. Baker, E. M. Stoudenmire, Kieron Burke, Steven R. White, Phys. Rev. B 90, 045109 (2014). [bibtex] [pdf] [doi]
[143] Guaranteed Convergence of the Kohn-Sham Equations Lucas O. Wagner, E. M. Stoudenmire, Kieron Burke, Steven R. White, Phys. Rev. Lett. 111, 093003 (2013). [bibtex] [pdf] [doi]
[140] Reference electronic structure calculations in one dimension Lucas O. Wagner, E.M. Stoudenmire, Kieron Burke, Steven R. White, Phys. Chem. Chem. Phys. 14, 8581 - 8590 (2012). [bibtex] [pdf] [doi]
[133] One-Dimensional Continuum Electronic Structure with the Density-Matrix Renormalization Group and Its Implications for Density-Functional Theory E.M. Stoudenmire, Lucas O. Wagner, Steven R. White, Kieron Burke, Phys. Rev. Lett. 109, 056402 (2012). [bibtex] [pdf] [doi]

Funding
This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC008696.

Current Student

Thomas Baker

Alumni

Lucas Wagner

E. M. Stoudenmire

Senior Collaborator

Steven White