Studies of Hubbard Clusters by Means of Static and Time-Dependent Density Functional Theory (TDDFT)


Thomas Roessler




Friday, 10 September 2010, 13:15
Matfys library

Abstract:
Understanding interacting systems in and out of equilibrium is a central problem in condensed matter physics. An important place in the pool of theoretical methods used to describe quantum matter is occupied by ground state density functional theory (DFT) and time-dependent density functional theory (TDDFT). In this thesis work, these DFT methods are applied to a lattice Hubbard cluster of small size, so that exact calculations can still be done and a so called "reverse engineering" technique can be applied to obtain the exact exchange-correlation potential. We will report of a quite unexpected result found during our study, namely that for a chosen set of parameters in our system, a singlet-triplet degenerate ground state occurs, where the density is not representable by non-interacting Kohn-Sham electrons in the ensemble sense. Furthermore, starting from a v0-representable singlet state (i.e. expressible in terms of a Kohn-Sham image), we will also show how TDDFT can approach such a problematic parameter region, via a time evolution in the adiabatic limit. This will provide further insight on the rather complex and non-local nature of the exchange-correlation functional.