# Heidelberg 2015 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 12: Quantum Gases: Bosons II

### Q 12.6: Vortrag

### Montag, 23. März 2015, 15:45–16:00, P/H2

**Ground states for the Bose-Hubbard model with flat bands** — •Petra Pudleiner^{1} and Andreas Mielke^{2} — ^{1}Institute of Physics, Johannes Gutenberg University, Mainz, Germany — ^{2}Institute for Theoretical Physics, Ruprecht-Karls University, Heidelberg, Germany

Flat band systems have been studied intensively in experiment and theory. They are a prototype for strongly correlated systems. Especially for bosons in a flat band, several interesting questions arise: What is the nature of the ground state? Are there regions in phase space where one can see a Bose transition?

The Bose-Hubbard model is used to visualize low energies on two-dimensional lattices which exhibit a lowest flat energy band. Up to the critical lattice filling constant, an eigenstate of the aforementioned band can be constructed by means of the charge density wave (CDW) as many-body ground state. Huber and Altman [1] explored ground states in the vicinity of the critical filling on the kagome lattice via a mean-field calculation; however, by restricting the calculation to a weakly interacting Hamiltonian.

The purpose of this talk is, firstly, to present similar results which are obtained by transferring their methods to the checkerboard lattice and, secondly, to demonstrate initial steps to extend to strong interactions. In this regard, one boson is added to the well-known ground state. The distribution of this additional particle seems to be localized, in contrast to the weakly interacting limit; here we observe a Bose condensation.

[1] S. Huber and E. Altman, PRB 82, 184502 (2010)