Spectral flow, condensate and topology in lattice QCD

We study the spectral how of the Wilson-Dirac operator H(m) with and withou t an additional Sheikholeslami-Wohlert (SW) term on a variety of SU(3) latt ice gauge field ensembles in the range 0 less than or equal to m less than or equal to 2. We have used ensembles generated from the Wilson gauge actio n, an improved gauge action. and several two-flavor dynamical quark ensembl es. Two regions in in provide a generic characterization of the spectrum. I n region I defined by m less than or equal to m(1), the spectrum has a gap. In region II defined by m(1) less than or equal to m less than or equal to 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 mono tonically with the crossing point down to a size of about one lattice spaci ng. These small modes are unphysical, and we find the topological susceptib ility is relatively stable in the part of region II where the small modes c ross. We argue that the lack of a gap in region II is expected to persist i n the infinite volume limit at any gauge coupling. The presence of a gap is important for the implementation of domain wall fermions. (C) 1998 Elsevie r Science B.V.