  In QCD chiral symmetry is explicitly broken by quark masses, the effect of
which can be described reliably by chiral perturbation theory. Effects of
explicit chiral symmetry breaking by the lattice regularisation of the Dirac
operator, typically parametrised by the residual mass, should be negligible for
almost all observables if the residual mass of the Dirac operator is much
smaller than the quark mass. However, maintaining a small residual mass becomes
increasingly expensive as the quark mass decreases towards the physical value
and the continuum limit is approached. We investigate the feasibility of using
a new approximately chiral Dirac operator with a small residual mass as an
alternative to overlap and domain wall fermions for lattice simulations. Our
Dirac operator is constructed from a Zolotarev rational approximation for the
matrix sign function that is optimal for bulk modes of the Hermitian kernel
Dirac operator but not for the low-lying parts of its spectrum. We test our
operator on various 32^3\times64 lattices, comparing the residual mass and the
performance of the Hybrid Monte Carlo algorithm at a similar lattice spacing
and pion mass with a hyperbolic tangent operator as used by domain wall
fermions. We find that our approximations have a significantly smaller residual
mass than domain wall fermions at a similar computational cost, and still admit
topological charge change.
