Theoretical foundation for the Index Theorem on the lattice with staggered fermions

Understand

A way to identify the would-be zero-modes of staggered lattice fermions away from the continuum limit is presented.

• Our approach also identifies the chiralities of these modes, and their index is seen to be determined by gauge field topology in accordance with the Index Theorem.
• The key idea is to consider the spectral flow of a certain hermitian version of the staggered Dirac operator.
• The staggered fermion index thus obtained can be used as a new way to assign the topological charge of lattice gauge fields.