  To investigate the light scalar tetraquark candidate $a_0(980)$ (quantum
numbers $J^P =0^+$), a correlation matrix including a variety of two- and
four-quark interpolating operators has to be computed. We discuss efficient
techniques to compute the elements of this correlation matrix, in particular
diagrams with closed quark loops. Furthermore, we present evidence that such
diagrams are not negligible given our precision, and their contribution is
essential to obtain physically meaningful results. In particular, we find
indications of the existence of an "additional" state around the two-particle
thresholds of $K+ \bar K$ and $\eta +\pi$, which could correspond to the
$a_0(980)$ meson.
