Study Of QCD Vacuum By Lattice Overlap Operator

The idea of the instanton-dominated QCD vacuum has solved many problems, but it still questionably. Nevertheless, QCD instanton remained rather popular as a frequently preferred way of thinking about vacuum topology. The instanton solution was used as a basis for developing a rather successful semiclassically-motivated phenomenology, instanton liquid model. This setup allows for an interesting mechanism of spontaneous chiral symmetry breaking. In this paper, we investigate this picture by lattice QCD.In the past, many people used cooling or smoothing to investigate the structure of lattice vacuum. But the cooling or smoothing has subjective nature, so the results obtained by this way are unreliable. In this paper, we use lattice Fermions to investigate the pure gluon field vacuum, i.e. we use a massless fermion to probe the structure of the vacuum. The vacuum severed as a background, and its properties can be reflected by the states of the fermion. So we can derive the structure of the vacuum from the low-lying eigenmodes of overlap operator of the massless fermion.The lattice size we calculated is 103.20, and the lattice spacing is a = 0.123 fm . The result we obtained is consistent with the instanton liquid model, i.e. the density of instantons is n = 1fm-4. In order to check our result, we use it to calculate the gluon condensate. The result is 2.1897 GeV4, which in agreement with the phenomenogical value.