This article may be too technical for most readers to understand.(September 2023) |
In lattice field theory, overlap fermions are a fermion discretization that allows to avoid the fermion doubling problem. They are a realisation of Ginsparg–Wilson fermions.
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 by the overlap Dirac operator
where is the ″kernel″ Dirac operator obeying , i.e. is -hermitian. The sign-function usually has to be calculated numerically, e.g. by rational approximations. [7] A common choice for the kernel is
where is the massless Dirac operator and is a free parameter that can be tuned to optimise locality of . [8]
Near 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.[ citation needed]
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