Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

TL;DR

This paper introduces a novel discretization method for Dirac fermions on lattices that avoids fermion doubling and preserves key symmetries, enabling detailed spectral analysis across multiple symmetry classes.

Contribution

It adapts Stacey discretization to create a generalized eigenproblem for Dirac fermions, maintaining symmetries and conservation laws crucial for accurate spectral studies.

Findings

Avoids fermion doubling in lattice Dirac models

Preserves chiral and symplectic symmetries

Enables spectral analysis across four symmetry classes

Abstract

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