  We propose an exactly solvable multisite interaction spin-1/2
Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous
studies of chaotic entanglement. By making use of the generalized star-triangle
transformation, we map the initial model onto an effective Ising one on a
Husimi lattice, which we solve then exactly by applying the recursive method.
Expressing the entanglement of the Heisenberg spins, that we quantify by means
of the concurrence, in terms of the magnetic quantities of the system, we
demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the
underlying chaos may slightly enhance the amount of the entanglement, and
present on the phase diagram the transition lines from the uniform to periodic
and from the periodic to chaotic regimes.
