The stability of ferromagnetism in the Hubbard model on two-dimensional line graphs

Abstract

The Hubbard model on line graphs has a flat band and highly degenerate ferromagnetic ground states. Here, we study the Hubbard model on a line graph of a planar bipartite graph by adding a special contribution to the kinetic energy which lifts the degeneracy of the lowest single particle state to a general Hamiltonian. We prove that, at half-filling of the lowest band and for sufficiently strong repulsion U, the ground states of this Hamiltonian remain saturated ferromagnetic for a class of line graphs of planar bipartite graphs.