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- Exact Calculations in the 1D Continuum for DFT and Beyond

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.

Collection/Series:

Event Type:

Seminar

Speaker(s):

Event Date:

Tuesday, November 27, 2012 - 14:00 to 15:30

Location:

Bob Room

©2012 Perimeter Institute for Theoretical Physics