##
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.