Lattice gauge action suppressing near-zero modes of HW

概要

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We propose a lattice action including unphysical Wilson fermions with a negative mass m0 of the order of the inverse lattice spacing. With this action, the exact zero mode of the Hermitian Wilson-Dirac operator HW(m0) cannot appear and near-zero modes are strongly suppressed. By measuring the spectral density rho(lambdaW), we find a gap near lambdaW=0 on the configurations generated with the standard and improved gauge actions. This gap provides a necessary condition for the proof of the exponential locality of the overlap-Dirac operator by Hernandez, Jansen, and Lüscher. Since the number of near-zero modes is small, the numerical cost to calculate the matrix sign function of HW(m0) is significantly reduced, and the simulation including dynamical overlap fermions becomes feasible. We also introduce a pair of twisted mass pseudofermions to cancel the unwanted higher mode effects of the Wilson fermions. The gauge coupling renormalization due to the additional fields is then minimized. The topological charge measured through the index of the overlap-Dirac operator is conserved during continuous evolutions of gauge field variables.
2006-11-03