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The conjecture that several recently observed mesons have a structure, which is not dominated by an ordinary quark-antiquark pair, but by a four-quark structure, is being actively investigated both theoretical and experimentally. Such a state may be characterized as a mesonic molecule or as a diquark-antidiquark pair. Lattice QCD provides a theoretically sound framework to study such states. To quantitatively investigate the internal structure of such mesons, one needs to precisely compute correlation matrices containing several interpolating operators including two and four quarks. Here we discuss certain technical aspects of such correlation matrices suited to study tetraquark candidates with $J^P = 0^+$ and flavor structure $q_1 \bar{q_2} q_3 \bar{q}_3$, e.g.\ the $a_0(980)$ meson, the $D_{s0}^\ast$ meson and some of the charged $c \bar{c}$ $X$ states. Some numerical results for the $a_0(980)$ meson are presented.

Computation of correlation matrices for tetraquark candidates with $J^P = 0^+$ and flavor structure $q_1 \bar{q_2} q_3 \bar{q}_3$