By Simon Hauswirth
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Extra info for Light hadron spectroscopy in quenched lattice QCD with chiral fixed-point fermions
This is computationally quite expensive due to the inversion of the Dirac operator which is needed and therefore increases the time for an iteration step in the minimization of χ2 considerably. The plot on the right-hand side of Fig. 4 shows that χ2GW from the Ginsparg-Wilson breaking seems to correlate highly with the χ2 from the propagator FP relation, so we did not pursue this path further. In order to parametrize the operator R in Eq. 14) we proceed in a similar way as for the Dirac operator.
1) should have a large overlap with the desired state. 3) are not expected to fulfill this criterion well, as they do not take into account the spatial extension of the hadron. 2 fm. 15) x,y where ϕ(x, y) is the wave function of the meson. 2) is reproduced. 15) are often referred to as smeared operators. They are in this form not gauge invariant quantities, and therefore their average over gauge configurations would vanish due to Elitzur’s theorem . To prevent that, one either has to include the parallel transporters in the operator or to work in a fixed gauge background.
In the final phase of this iterative procedure, some of the naive continuum limit constraints on the parameters of the Dirac operator are released. Furthermore, in the last blocking step a low-order overlap expansion is applied to the parametrization which is put into the right hand side in order to reduce the remaining fluctuations of the small eigenvalues even further . Let us make a few comments on this procedure of iteratively finding the parameters for the FP Dirac operator at lattice spacings typically used in simulations.