Dresden 2009 – wissenschaftliches Programm
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O: Fachverband Oberflächenphysik
O 41: Ab-initio approaches to excitations in condensed matter I
O 41.5: Vortrag
Mittwoch, 25. März 2009, 16:00–16:15, SCH 251
Towards a low-dimensional Lieb-Oxford bound — •César R. Proetto1,2, Klaus Capelle3, Stefano Pittalis1, and Esa Räsänen4 — 1Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany and European Theoretical Spectroscopy Facility (ETSF) — 2Centro Atómico Bariloche and Instituto Balseiro, 8400 S. C. de Bariloche, Río Negro, Argentina — 3Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, São Paulo, 13560-970, Brazil — 4Nanoscience Center, Department of Physics, P. O. Box 35 FIN-40014 University of Jyväskylä, Finland
Exact constraints on the unknown exchange-correlation (xc) energy functional are of fundamental importance in density-functional theory (DFT): One main and successful strategy in the never-ending challenge for the building of more accurate xc functionals consist of satisfying as many exact constraints as possible. The Lieb-Oxford bound (LOB) for three-dimensional (3D) systems is one of such exact constraints, and in its more useful version within the context of DFT is given as a lower bound on the correlation energy, in terms of a power of the particle density. For the bound to be useful, it should be as tight as possible. In this talk, we will provide the construction of the equivalent of the 3D LOB, but for the low-dimensional cases. In particular, by using scaling analysis and exploiting the fact that for some low-dimensional systems we known the ground-state xc energy and density, we have computed the expression for the bound in the 1D and 2D cases, and analyzed in detail the dimensionality crossover in between.