Fermions without fermi fields

Abstract

It is shown that an arbitrary Fermion hopping hamiltonian can be represented by a system with no fermion fields, generalising earlier results by M. Levin & X.G. Wen [Phys Rev B 67, 245316 (2003)]. All the operators in the hamiltonian of resulting description obey the principle of locality, that operators associated with different sites commute, despite the system having excitations obeying Fermi statistics. Whilst extra conserved degrees of freedom are introduced, they are all locally identified in the representation obtained. The same methods apply to Majorana (half) fermions, which for cartesian lattices mitigate the Fermion Doubling Problem. The generality of these results suggests that the observation of Fermion excitations in nature does not demand that anticommuting Fermion fields are fundamental.