NUMERICAL STUDY OF THE S = 1 ANTIFERROMAGNETIC SPIN CHAIN WITH BOND ALTERNATION

We study the S=1 quantum spin chain with bond alternation H = SIGMA(i)(1-(-1)idelta) S(i).S(i+1) by the density matrix renormalization group method recently proposed by White (Phys. Rev. Lett. 69 (1992) 2863). We find a massless point at delta(c) = 0.25 +/- 0.01. We also find the edge states in the region delta < delta(c) under the open boundary condition, which disappear in the region delta > delta(c). At the massless point, the spin wave velocity v(s) 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 delta = 6, accompanying breaking of the hidden Z2 x Z2 symmetry.