Evaluation of the continuum limit of the axial anomaly and index is sketched for the staggered overlap Dirac operator. There are new complications compared to the usual overlap case due to the distribution of the spin and flavor components around lat
tice hypercubes in the staggered formalism. The index is found to correctly reproduce the continuum index, but for the axial anomaly this is only true after averaging over the sites of a lattice hypercube.
Results on the computational efficiency of 2-flavor staggered Wilson fermions compared to usual Wilson fermions in a quenched lattice QCD simulation on $16^3times32$ lattice at $beta=6$ are reported. We compare the cost of inverting the Dirac matrix
on a source by the conjugate gradient (CG) method for both of these fermion formulations, at the same pion masses, and without preconditioning. We find that the number of CG iterations required for convergence, averaged over the ensemble, is less by a factor of almost 2 for staggered Wilson fermions, with only a mild dependence on the pion mass. We also compute the condition number of the fermion matrix and find that it is less by a factor of 4 for staggered Wilson fermions. The cost per CG iteration, dominated by the cost of matrix-vector multiplication for the Dirac matrix, is known from previous work to be less by a factor 2-3 for staggered Wilson compared to usual Wilson fermions. Thus we conclude that staggered Wilson fermions are 4-6 times cheaper for inverting the Dirac matrix on a source in the quenched backgrounds of our study.
A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces the four
quark flavors described by the staggered fermion to two quark flavors; this pair can be taken as the up and down quarks in Lattice QCD. The exact flavored chiral symmetry of the staggered fermion gets converted into an unflavored Ginsparg-Wilson chiral symmetry of the new overlap fermion, which also has pairs of exact chiral zero-modes satisfying the Index Theorem. Stability under radiative corrections is checked. A domain wall formulation giving a truncation of this overlap construction is also outlined.
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 accor
dance 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. In a numerical study in U(1) backgrounds in 2 dimensions it is found to perform as well as the Wilson index while being computationally more efficient. It can also be expressed as the index of an overlap Dirac operator with a new staggered fermion kernel.
