Pseudo-Dirac Hamiltonians and Flux Phases of SU(N) magnets

The lattice Dirac Hamiltonian describes a particle hopping on a lattice in a particular background magnetic field. We present a family of hopping Hamiltonians in other background fields that generalize many aspects of the Dirac Hamiltonian to lines and planes of nodes. In our canonical case, hopping on the pyrochlore lattice gives rise to a half filled fermi surface that consists of four intersecting [111] lines. This spectrum is invariant under tetrahedral rotations, rather than all rotations as in the Dirac case, resulting in a more complex matrix anti-commutation structure. This structure arises in a large N treatment of the SU(N) Heisenberg model on the pyrochlore.