  We investigate the production of exotic tetraquarks, $QQ\bar{q}\bar{q} \equiv
T_{QQ}$ ($Q=c$ or $b$ and $q=u$ or $d$), in relativistic heavy-ion collisions
using the quark coalescence model. The $T_{QQ}$ yield is given by the overlap
of the density matrix of the constituents in the emission source with the
Wigner function of the produced tetraquark. The tetraquark wave function is
obtained from exact solutions of the four-body problem using realistic
constituent models. The production yields are typically one order of magnitude
smaller than previous estimations based on simplified wave functions for the
tetraquarks. We also evaluate the consequences of the partial restoration of
chiral symmetry at the hadronization temperature on the coalescence
probability. Such effects, in addition to increasing the stability of the
tetraquarks, lead to an enhancement of the production yields, pointing towards
an excellent discovery potential in forthcoming experiments. We discuss further
consequences of our findings for the search of exotic tetraquarks in central
Pb+Pb collisions at the LHC.
