# Berlin 2012 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# KR: Fachgruppe Kristallographie

## KR 5: Poster I – including Multiferroics (MA with DF, DS, KR, TT)

### KR 5.46: Poster

### Dienstag, 27. März 2012, 12:15–15:15, Poster A

**Bose-Hubbard model on two-dimensional line graphs** — •Johannes Motruk and Andreas Mielke — Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg

We investigate the positive hopping bosonic Hubbard Model on line graphs of finite 2-connected planar bipartite graphs. The model on these lattice geometries exhibits flat bands and the single- as well as many-particle ground states are highly degenerate. Using notions from graph theory, we are able to give a basis for the space of many-particle ground states. The particles in these states are localized on vertices of the line graph which are edges of the original graph belonging to edge-disjoint cycles. This construction works up to a certain critical filling factor at which the cycles are close-packed. We rigorously show the linear independence of these states and prove that they span the space of many-particle ground states.

Furthermore, we establish that the entropy per lattice site in the ground state with constant (except critical) filling factor remains finite in the thermodynamic limit. Some of our findings can be applied to spin models of quantum antiferromagnets at high fields on the considered lattices.