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In terms of spinless fermions and spin waves, we describe magnetic propertiesof a spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chain whichbehaves as a Haldane-gap antiferromagnet. On one hand, we employ theJordan-Wigner transformation and treat the fermionic Hamiltonian within theHartree-Fock approximation. On the other hand, we employ the Holstein-Primakofftransformation and modify the conventional spin-wave theory so as to restorethe sublattice symmetry. We calculate the excitation gap, the specific heat,the magnetic susceptibility, magnetization curves, and the nuclear spin-latticerelaxation rate with varying bond alternation. These schemes are furtherapplied to a bond-alternating tetramerized chain which behaves as aferrimagnet. The fermionic language is particularly stressed as a useful toolto investigate one-dimensional spin-gapped antiferromagnets, while the bosonicone works better for ferrimagnets.Comment: 10 pages, 5 figure

Fermionic versus bosonic descriptions of one-dimensional spin-gapped antiferromagnets