Fractional charges in pyrochlore lattices

Abstract. A pyrochlore lattice is considered where the average electron number of electrons per site is half–integer, concentrating on the case of exactly half an electron per site. Strong on-site repulsions are assumed, so that all sites are either empty or singly occupied. Where there are in addition strong nearest–neighbour repulsions, a tetrahedron rule comes into effect, as previously suggested for magnetite. We show that in this case, there exist excitations with fractional charge ±e/2. These are intimately connected with the high degeneracy of the ground state in the absence of kinetic energy terms. When an additional electron is inserted into the system, it decays into two point like excitations with charge −e/2, connected by a Heisenberg spin chain which carries the electron’s spin.