Berlin 2018 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 72: Poster Session: Correlated Electrons
TT 72.83: Poster
Mittwoch, 14. März 2018, 15:00–19:00, Poster B
Variational approach to models with strongly correlated electrons — •Philip Mirbach1, Malte Schüler1,2, Tim Wehling1,2, and Gerd Czycholl1 — 1Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany — 2Bremen Center for Computational Materials Science, Universität Bremen, Am Fallturm 1a, 28359 Bremen, Germany
Electronic systems with strong interactions are promising materials for a wide variety of applications. These strongly correlated electron systems are often described by lattice models such as the Hubbard model. However, they are difficult to treat numerically.
We use Feynman's Variational Principle to determine optimal effective model systems that can be solved exactly, for example by ED-methods. We divide the original model into exactly solvable clusters, where the partition and the parameters are optimized by the variational principle. Internal correlation effects are correctly considered in these clusters. In addition, they maintain effective influences of the originally neglected interactions through the variation. The trivial case of completely decoupled clusters is equal to the Hartree-Fock (HF) approximation. Therefore, more complex effective model systems lead to systematic improvements beyond HF. By an optimal choice of the representation of the model, e. g. in real or momentum space, particularly effective parameters for describing the original model can be found.
Using the one-dimensional Hubbard model with four sites as an example, we show the possibilities of this method and compare the results with HF and the exact solution.