Dimerizations in spin-$S$ antiferromagnetic chains with three-spin interaction

We discuss spin-$S$ antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest interactions, and bond alternation. First, we prove rigorouslly that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitral $S$. Next, we discuss the ground state phase diagram of the models by introducing several effective field theories and universality classes of the transitions are described by the level-$2S$ $\mathrm{SU}(2)$ Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of $S=1$ and $S=3/2$ systems by using exact diagonalization and level spectroscopy method.