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Multiflavour mixtures of ultracold fermionic atoms on optical lattices provide unique opportunities for studying a wide range of correlation effects with direct access to the relevant control parameters. This has already been demonstrated for the paramagnetic Mott metal-insulator transition; it is expected that also the generic low-temperature antiferromagnetism (or at least precursors thereof) will soon be seen in 2-flavour experiments, possibly using the detection scheme developed in this project [1]. Once this milestone is accomplished, cold-atom systems may serve as quantum simulators of strongly correlated materials and, thereby, help solve both fundamental and technically relevant open questions in this field. The central goal of this project is to develop appropriate theoretical tools for cold-atom specific aspects of correlation physics and to explore both the analogies and fundamental differences between correlated cold-atom systems and materials, with a specific focus on genuine multi-flavor effects.
Due to their tunability, cold-atom systems also appear as natural systems for controlled studies of flavor inequivalence, frustration, and of local inhomogeneities. We are going to address fundamental questions such as the relation between lattice types, the number of flavors and the resulting frustration effects (e.g. a triangular lattice is frustrated for 2-flavor mixtures, but not for balanced 3-flavor mixtures). Moreover, we will predict how a single impurity or few impurities alter the correlation physics in inhomogeneous systems. Selected issues will be studied in a direct material context, in close collaboration with TR49 projects belonging to subject area B Solid State Real Materials.
[1] E. V. Gorelik, I. Titvinidze, W. Hofstetter, M. Snoek, and N. Blümer, Néel transition of lattice fermions in a harmonic trap: a real-space dynamical mean-field study, Phys. Rev. Lett. 105, 065301 (2010) [arXiv:1004.4857].
Prerequisites: Solid background in condensed matter theory, experience with quantum many-body problems (ideally including Hubbard type models), programming skills.
| 2002 - 2006 | Carsten Knecht: Numerical and analytical approaches to strongly correlated electron systems (co-supervised, main supervisor: Prof. van Dongen). |
| 2006 - 2010 | Eberhard Jakobi: Numerische und analytische Untersuchungen stark korrelierter fermionischer Mehrbandsysteme. |
Voraussetzungen:
Prerequisites: