Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice
arXiv:hep-lat/9806032 · doi:10.1016/S0550-3213(98)00826-8
Abstract
We study the role of the O(a)-improving clover term for the spectrum of the lattice Dirac operator using cooled and thermalized SU(2) gauge field configurations. For cooled configurations we observe improvement of the spectral properties when adding the clover term. For the thermalized case (12^4, beta = 2.4) without clover term we find a rather bad separation of physical and doubler branches making a probabilistic interpretation of the Atiyah-Singer index theorem on the lattice questionable for this beta and lattice size. Adding the clover term leads to the creation of additional real eigenvalues which come in pairs of opposite chirality thus further worsening the situation for the index theorem.
Revised version, to appear in Nucl. Phys. B; discussion reworded, References updated
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- Convergence Rate and Locality of Improved Overlap Fermions
- Chiral symmetry restoration and the Z3 sectors of QCD
- Acceleration of the Arnoldi method and real eigenvalues of the non-Hermitian Wilson-Dirac operator
- 3D N = 1 SYM Chern-Simons theory on the Lattice
- Remnant index theorem and low-lying eigenmodes for twisted mass fermions
- Hadron spectroscopy of twisted mass lattice QCD at beta = 6.0
- Unquenching the topological susceptibility with an overlap action