Numerical Study of theS=1 Antiferromagnetic Spin Chain with Bond Alternation

We study the $S=1$ quantum spin chain with bond alternation H=∑ ᵢ (1-(-1)ⁱδ)Sᵢ· Sᵢ₊₁ by the density matrix renormalization group method recently proposed by Steven R. White ({69}{3844}{1993}). We find a massless point at δ c =0.25 ± 0.01. We also find the edge states in the region δ <δc under the open boundary condition, which disappear in the region δ >δ c. At the massless point, the spin wave velocity vₛ is 3.66 ± 0.10 and the central charge c is 1.0± 0.15. Our results indicate that a continuous phase transition occurs at the massless point δ =δc accompanying breaking of the hidden Z₂× Z₂ symmetry.