Alternating spin chains with singlet ground states

We investigate low-energy properties of the alternating-spin-chain model composed of spins $s_1$ and $s_2$ with a singlet ground state. After examining the spin-wave spectrum in detail, we map low-energy spin excitations to the O(3) nonlinear σ model in order to take into account quantum fluctuations. Analyzing the topological term in the resulting σ model, we discuss how the massless or massive excitations are developed, especially according to the topological nature of the alternating spin system.