Analytic Smearing of SU(3) Link Variables in Lattice QCD

Abstract

An analytic method of smearing link variables in lattice QCD is proposed and tested. The differentiability of the smearing scheme with respect to the link variables permits the use of modern Monte Carlo updating methods based on molecular dynamics evolution for gauge-field actions constructed using such smeared links. In examining the smeared mean plaquette and the static quark-antiquark potential, no degradation in effectiveness is observed as compared to link smearing methods currently in use, although an increased sensitivity to the smearing parameter is found.

Figures (4)

• Figure 1: The expansion up to first order in the $\rho_{\mu\nu}$ of the new link variable $U^{(1)}$ in terms of paths of the original links. Each closed loop includes a trace with a factor $1/N$ in $SU(N)$.
• Figure 2: The effective energy $aE_{\rm eff}(r)$ defined in Eq. (\ref{['eq:Eeff']}) for a static quark-antiquark pair separated by a distance $r=5a$ for several levels of smearing $n_\rho=1,5,$ and $20$ against the smearing parameter $\rho$. These results were obtained on a $12^4$ lattice using the Wilson gauge action with coupling $\beta=5.7$. Curves labeled $A_{n_\rho}$ indicate results using the spatially-isotropic three-dimensional version of the analytic stout link smearing scheme with $n_\rho=1,5,$ and $20$ levels, while the curves labeled $B_{n_\rho}$ show the results for links smeared using Eq. (\ref{['eq:Ufuzz']}) with the projection method of Ref. su3projectA.
• Figure 3: The effective energy $aE_{\rm eff}(r)$ defined in Eq. (\ref{['eq:Eeff']}) for a static quark-antiquark pair separated by a distance $r=10a$ for several levels of smearing $n_\rho=1,5,$ and $20$ against the smearing parameter $\rho$. Results were obtained on a $24^4$ lattice using the Wilson gauge action with coupling $\beta=6.2$. Curves labeled $A_{n_\rho}$ indicate results using the spatially-isotropic three-dimensional version of the analytic stout link smearing scheme with $n_\rho=1,5,$ and $20$ levels, while the curves labeled $B_{n_\rho}$ show the results for links smeared using Eq. (\ref{['eq:Ufuzz']}) with the projection method of Ref. su3projectA.
• Figure 4: The mean smeared plaquette against the smearing parameter $\rho$. These results were obtained using the Wilson gauge action on a $12^4$ lattice with coupling $\beta=5.7$. Curves labeled $A_{n_\rho}$ indicate results obtained using the isotropic four-dimensional version of the analytic stout link smearing scheme with $n_\rho=1$ and $5$ levels, while the curves labeled $B_{n_\rho}$ show the results with links smeared using Eq. (\ref{['eq:Ufuzz']}) and the projection method of Ref. su3projectA.