  Time reversal symmetric topological insulators are generically robust with
respect to weak local interaction, unless symmetry breaking transitions take
place. Using dynamical mean-field theory we solve an interacting model of
quantum spin Hall insulators and show the existence, at intermediate coupling,
of a symmetry breaking transition to a non-topological insulator characterised
by exciton condensation. This transition is of first order. For a larger
interaction strength the insulator evolves into a Mott one. The transition is
continuous if magnetic order is prevented, and notably, for any finite Hund's
exchange it progresses through a Mott localization before the condensate
coherence is lost. We show that the correlated excitonic state corresponds to a
magneto-electric insulator which allows for direct experimental probing.
Finally, we discuss the fate of the helical edge modes across the excitonic
transition.
