  We show that spin S Heisenberg spin chains with an additional three-body
interaction of the form (S_{i-1}S_{i})(S_{i}S_{i+1})+h.c. possess fully
dimerized ground states if the ratio of the three-body interaction to the
bilinear one is equal to 1/(4S(S+1)-2). This result generalizes the
Majumdar-Ghosh point of the J_1-J_2 chain, to which the present model reduces
for S=1/2. For S=1, we use the density matrix renormalization group method
(DMRG) to show that the transition between the Haldane and the dimerized phases
is continuous with central charge c=3/2. Finally, we show that such a
three-body interaction appears naturally in a strong-coupling expansion of the
Hubbard model, and we discuss the consequences for the dimerization of actual
antiferromagnetic chains.
