Abstract
We use the density matrix renormalization group method to study the ground-state "phase" diagram and some low-energy properties of an antiferromagnetic spin-1 chain with a next-nearest-neighbour exchange J2 and an alternation δ of the nearest-neighbour exchanges. We find a line running from a gapless point at (J2,δ) = (0,0.25 ± 0.01) up to a "gapless" point at (0.73 ± 0.005,0) such that the open-chain ground state is fourfold degenerate below the line and is unique above it. A disorder line 2J2 + δ = 1 runs from δ = 1 to about δ = 0.136. To the left of this line, the peak in the structure factor S(q) is at π, while to the right of the line, it is at less than π.