Dumbbell Fermions and Spin Models on Honeycomb Lattices

Abstract

We express Kitaev's exact solution of spin models on the honeycomb lattice as a special case of a higher dimensional duality between staggered Majorana fermions and Pauli spins. General models with bilinear nearest neighbor couplings of spins and external magnetic fields are soluble in this way. Each model gives rise to an infinite number of single particle fermion Schrodinger equations, depending on the choice of discrete gauge field flux.

Comments: The bilinears in fermion parities all commute with the Hamiltonian, but not with each other, so cannot be simultaneously diagonalized. The models do not reduce to bilinears in fermions