  We propose a lattice action including unphysical Wilson fermions with a
negative mass m_0 of the order of the inverse lattice spacing. With this
action, the exact zero mode of the hermitian Wilson-Dirac operator H_W(m_0)
cannot appear and near-zero modes are strongly suppressed. By measuring the
spectral density rho(lambda_W), we find a gap near lambda_W=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 Luescher. Since the number of
near-zero modes is small, the numerical cost to calculate the matrix sign
function of H_W(m_0) is significantly reduced, and the simulation including
dynamical overlap fermions becomes feasible. We also introduce a pair of
twisted mass pseudo-fermions 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.
