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A way to identify the would-be zero-modes of staggered lattice fermions awayfrom the continuum limit is presented. Our approach also identifies thechiralities of these modes, and their index is seen to be determined by gaugefield topology in accordance with the Index Theorem. The key idea is toconsider the spectral flow of a certain hermitian version of the staggeredDirac operator. The staggered fermion index thus obtained can be used as a newway to assign the topological charge of lattice gauge fields. In a numericalstudy in U(1) backgrounds in 2 dimensions it is found to perform as well as theWilson index while being computationally more efficient. It can also beexpressed as the index of an overlap Dirac operator with a new staggeredfermion kernel.

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