Spin-wave series for quantum one-dimensional ferrimagnets

Second-order spin-wave expansions are used to compute the ground-state energy and sublattice magnetizations of the quantum one-dimensional Heisenberg ferrimagnet with nearest-neighbor antiferromagnetic interactions and two types of alternating sublattice spins $S_1>S_2$. It is found that in the extreme quantum cases $(S_1,S_2)=(1,1/2)$, $(3/2,1)$, and $(3/2,1/2)$, the estimates for the ground-state energy and sublattice magnetizations differ less than 0.03% for the energy and 0.2% for the sublattice magnetizations from the recently published density matrix renormalization group numerical calculations. The reported results strongly suggest that the quantum Heisenberg ferrimagnetic chains give another example of a low-dimensional quantum spin system where the spin-wave approach demonstrates a surprising efficiency.