Initially introduced by Neuberger in 1998,[1] they were quickly taken up for a variety of numerical simulations.
[2][3][4] By now overlap fermions are well established and regularly used in non-perturbative fermion simulations, for instance in lattice QCD.
[5][6] Overlap fermions with mass
are defined on a Euclidean spacetime lattice with spacing
The sign-function usually has to be calculated numerically, e.g. by rational approximations.
is a free parameter that can be tuned to optimise locality of
the overlap Dirac operator recovers the correct continuum form (using the Feynman slash notation) whereas the unphysical doublers near
are suppressed by a high mass and decouple.
Overlap fermions do not contradict the Nielsen–Ninomiya theorem because they explicitly violate chiral symmetry (obeying the Ginsparg–Wilson equation) and locality.