  Using a hybrid method based on fermionic diagonalization and classical Monte
Carlo, we investigate the interplay between itinerant and localized spins, with
competing double- and super-exchange interactions, on a honeycomb lattice. For
moderate superexchange, a geometrically frustrated triangular lattice of
hexagons forms spontaneously. For slightly larger superexchange a dimerized
groundstate is stable that has macroscopic degeneracy. The presence of these
states on a non-frustrated honeycomb lattice highlights a novel phenomenon in
this itinerant electron system: emergent geometrical frustration and
degeneracy.
