Quantum phase transition in double triangular layer

We study a quantum spin model defined on a double triangular layer whose ground state and the first few excited states could be rigorously obtained for any spin S. There exist two kinds of ground state, one is a complete dimerized state, and the other one is the ground state of corresponding spin-2S model defined on the single triangular layer. Quantum phase transition points are determined by the spin-wave theory and verified by exact diagonalization study of finite clusters. The excitation spectrum is investigated and we found that there exists a singlet to singlet transition as well as triplet to singlet transition as parameters vary.