Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD

A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multihadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. ${Z}_{N}$ noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise-dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin $I=0$, 1, 2 on large anisotropic ${24}^{3}\ifmmode\times\else\texttimes\fi{}128$ lattices with spatial spacing ${a}_{s}$\sim${}0.12\text{ }\text{ }\mathrm{fm}$ and temporal spacing ${a}_{t}$\sim${}0.034\text{ }\text{ }\mathrm{fm}$ for pion masses ${m}_{$\pi${}}$\approx${}390$ and 240 MeV.