Research On Hopping Parameter Expansion Combined With Noise Method In Lattice QCD

In this paper,the basic knowledge of lattice quantum chromodynamics is briefly reviewed,and the numerical simulation in lattice quantum chromodynamics is introduced.Then the application of hopping parameter expansion to reducing the statistical error caused by the noise method is investigated.By combining the hopping parameter expansion with the noise method,we have reduced the statistical error induced when using the noise method to calculate the disconnected contributions.We compare the standard deviation of the results obtained by using the noise method directly and that of the results obtained by using the hopping parameter expansion.We find that the results obtained by using the hopping parameter expansion are better than the results obtained by only using the noise method,and that the effectiveness of the hopping parameter expansion is enhanced as the expansion order increases.For the trace of the inverse of Wilson’s Dirac operator,HPE can reduce the statistical error by about 60%.In addition,we study the effectiveness of hopping parameter expansion on the reduction of statistical error for different values of k,and find that the effectiveness of hopping parameter expansion decreases when k gets bigger.Finally,we derive two formulae for fast calculation of two even terms in the hopping parameter expansion and prove that some disconnected contributions in the lattice calculation is real or imaginary.