Overlap

The intention of these notes is to outline how we construct the overlap operator in the gwu-qcd framework. The overlap operator preserves chiral symmetry on the lattice, and is the most ideal operator used to explore low pion masses. The massless overlap is defined by

\(\mathbf{D_0} = \rho(1+\gamma_5)\varepsilon(H)\)

Where \(\rho= 4 - 1/2\kappa\), \(\kappa \) is a positive number. \(H\) is the hermitian Wilson operator, and \(\epsilon(H)\) is the matrix sign function. Given a vector \(\vec{\eta}\), we want to compute the solution \(\vec{x}\), which is the matrix vector multiplication

\(\mathbf{D_0} \vec{\eta} = \vec{x} \)