We study the spectral flow of the Wilson-Dirac operator H(m) with and without
an additional Sheikholeslami-Wohlert (SW) term on a variety of SU(3) lattice
gauge field ensembles in the range 0≤m≤2. We have used ensembles
generated from the Wilson gauge action, an improved gauge action, and several
two-flavor dynamical quark ensembles. Two regions in m provide a generic
characterization of the spectrum. In region I defined by m≤m1, the
spectrum has a gap. In region II defined by m1≤m≤2, the gap is
closed. The level crossings in H(m) that occur in region II correspond to
localized eigenmodes and the localization size decreases monotonically with the
crossing point down to a size of about one lattice spacing. These small modes
are unphysical, and we find the topological susceptibility is relatively stable
in the part of region II where the small modes cross. We argue that the lack of
a gap in region II is expected to persist in the infinite volume limit at any
gauge coupling. The presence of a gap is important for the implementation of
domain wall fermions.Comment: 30 pages latex with 13 postscript figures included by epsf. Expanded
discussion on domain wall fermions. Two figures have been bitmapped to reduce
size. Originals are in http://www.scri.fsu.edu/~edwards/su3_to