Constructing static quark-antiquark creation operators from Laplacian eigenmodes

We investigate static quark-antiquark operators based on trial states formed from eigenvectors of the covariant three-dimensional lattice Laplace operator. We test the method by computing the static quark-antiquark potential and comparing results to standard Wilson loop measurements. The new method is efficient not only for on-axis, but also for many off-axis quark-antiquark separations when a fine spatial resolution is required. We further improve the ground-state overlap by using multiple eigenvector pairs, weighted with Gaussian profile functions of the eigenvalues, providing a variational basis. The method presented here can be applied to potential functions for all possible excitations of a gluonic string with fixed ends, hybrid or tetraquark potentials, as well as static-light systems and allows visualization of the spatial distribution of the Laplace trial states.