Exact ferromagnetic ground states of multi-band Hubbard models

Akinori Tanaka, Toshihiro Idogaki

Akinori Tanaka, Hal Tasaki

Makoto Homma, Chigak Itoi

M. Gulácsi, György Kovács, Zsolt Gulácsi

We model conducting pentagon chains with a multi-orbital Hubbard model and prove that well below half filling, exact ferromagnetic ground states appear. The rigorous method we use is based on the transformation of original hamiltonian into positive semidefinite form. This technique is independent of the spatial dimension and does not require integrability of the model. The obtained ferromagnetism is connected to dispersionless bands but in a much broader sense than flat-band ferromagnetism requires, where on every site a Hubbard term is present. In our case, only a small percentage of, even randomly distributed, sites are only interacting.

Mario Salerno

Andreas Mielke

Let L(G) be the line graph of a graph G=(V,E). The Hubbard model on L(G) has ferromagnetic ground states with a saturated spin if the interaction is repulsive (U>0) and if the number of electrons N satisfies N>or=M. M= mod E mod + mod V mod -1 if G is bipartite and M= mod E mod + mod V mod otherwise. The author shows that the ferromagnetic ground state is unique if N=M. Further he gives a sufficient condition for the existence of other ground states if N>M. The results are valid also for a multi-band Hubbard model on a bipartite graph. In the case of a periodic lattice, the results are related to the existence of a flat energy band.