Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

The spatial discretization of the single-cone Dirac Hamiltonian on surface a topological insulator or superconductor needs special "staggered" grid, to avoid appearance spurious second cone in Brillouin zone. We adapt Stacey from lattice gauge theory produce generalized eigenvalue problem, form ${\mathcal H}\psi=E {\mathcal P}\psi$, with Hermitian tight-binding operators H}$, P}$, locally conserved particle current, and preserved chiral symplectic symmetries. This permits study spectral statistics fermions each four symmetry classes A, AII, AIII, D.