Studying Density Functional Theory and One-Dimensional Electronic Structure with DMRG

Miles Stoudenmire, University of California, Irvine

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, primarily 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 can treat realistic 3d systems efficiently, and has great predictive power when electrons are weakly correlated. But most established DFT approximations fail for strongly correlated systems. Improving DFT directly in 3d 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. At the simplest level, we can compare exact DMRG results to various DFT approximations. We can also compute exact quantities at the heart of DFT, including the Kohn-Sham system and the exact density functional. I will conclude by discussing some of the key questions we are investigating, including the ability of DFT approximations to predict gaps and transport properties. 

Video links: Part I, Part II, Part III

Part I

Part II

Part III

Ying-Jer Kao,
Dec 12, 2012, 5:12 PM