PIRSA:12110085

Exact Calculations in the 1D Continuum for DFT and Beyond

(2012). Exact Calculations in the 1D Continuum for DFT and Beyond. Perimeter Institute. https://pirsa.org/12110085

Exact Calculations in the 1D Continuum for DFT and Beyond. Perimeter Institute, Nov. 27, 2012, https://pirsa.org/12110085 

          @misc{ pirsa_PIRSA:12110085,
            doi = {10.48660/12110085},
            url = {https://pirsa.org/12110085},
            author = {},
            keywords = {},
            language = {en},
            title = {Exact Calculations in the 1D Continuum for DFT and Beyond},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {nov},
            note = {PIRSA:12110085 see, \url{https://pirsa.org}}
          }
Talk numberPIRSA:12110085
DOI10.48660/12110085
Collection
Talk Type Scientific Series

Abstract

Most applications of the density matrix renormalization group (DMRG) have been to lattice models with short range interactions. But recent developments in DMRG technology open the door to studying continuum systems with long-range interactions in one dimension (1d). One key motivation is simulating cold atom experiments, where it is possible to engineer Hamiltonians of precisely this type.   We have been applying DMRG in the 1d continuum with another motivation: to investigate and improve density functional theory (DFT). DFT has exact mathematical foundations, but in practice one must use approximations. These approximations work incredibly well for weakly correlated systems yet fail when correlations are strong.   Improving DFT directly for realistic 3d systems is hard because few systems can be solved exactly. By working in the 1d continuum instead, we can use the power of DMRG to study DFT. We can implement both the exact DFT formalism and standard DFT approximations. After showing how to overcome the challenges in performing these calculations, I will discuss some of the key questions we are investigating, for example, the ability of DFT to predict gaps of insulating systems.