We study the one-dimensional Heisenberg spin-$1∕2$ alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and the density matrix renormalization group method, we discuss how the system approaches the AF uniform spin-1 chain under certain conditions. When the ratio of AF to FM coupling strengths, $\alpha$ $(\alpha =J_{AF}∕J_F)$, is very small, physical properties of the alternating bond chain such as spin-spin correlation, the string correlation function, and the spin density coincide with those of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with the small $\alpha$ limit. In addition, the Haldane gap of the AF uniform spin-1 chain is four times the gap of the system considered.

• Received 31 August 2004

DOI:https://doi.org/10.1103/PhysRevB.71.054413