Stefan Schenk
Density functional theory on a lattice
Supervisor: Priv.-Doz. Dr. Peter Schwab [Theoretical physics II]
Date of oral examination: 07/16/2009
98 pages, english
In this work we study one-dimensional lattice models in order to investigate the applicability and accuracy of density functional theory. In particular we study the density-density response function as obtained within the adiabatic local density approximation (ALDA) and the exact-exchange approximation and compare it with known exact results. Furthermore we introduce current density functional theory (CDFT) for lattice models which allows us to construct a non-local frequency-dependent exchange-correlation potential. We find that CDFT+ALDA reproduces surprisingly well some of the characteristic features of the Luttinger liquid, for example the dispersion of the collective charge excitations, but it fails even qualitatively outside the long-wavelength low-frequency regime. This includes a dramatic underestimation of the backscattering process. Thus the local density approximation is not suitable for an accurate description of transport. The exact-exchange approximation shows a better description of the backscattering process. In a further step we discuss the transport through a small interacting region coupled to two leads by means of the linear conductance. We find that the local density approximation dramatically overestimates the resonances and that the exact-exchange approximation is a suitable approach for weak interaction. In addition we introduce a procedure which uses exact diagonalizations of small systems to obtain good exchange-correlation potentials for such transport problems.