Antiferromagnetic Spin Chain with Bond Alternation

i(1 − (−1)δ)Si · Si+1 by the density matrix renormalization group method recently proposed by Steven R. White (Phys. Rev. Lett. 69 (1993) 3844). We find a massless point at δc = 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 > δc. 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.