Phase transitions in antiferromagnetic quantum spin chains with bond alternation

We study the phase transitions in antiferromagnetic quantum spin chains with bond alternation, H=J Sigma(i)[1-(-1)(i) delta]S-i . S-i+1, of spin S=1, 3/2, and 2. On the one hand, using a transfer matrix technique, we make a simple variational approach, which results in the better estimates of the transition points than by the O(3) nonlinear-sigma-model quantum field theory. On the other hand, employing a quantum Monte Carlo method, we calculate the generalized string order parameter, O-string(z)(theta)=limL-->infinity O-string(z)(theta;L) with O-string(z)(theta;L)=[S-L/4(z) Pi(j=L/4)(3L/4-1) exp[i theta S-j(z)]S-3L/4(z)]. It turns out that the transition points are successfully detected by observing the overall behavior of O-string(z)(theta) at various values of delta. Investigating the dependences of O-string(z)(theta;L) on theta, L, and S, we discuss the applicability of the valence-bond-solid picture to the ground states of the present Hamiltonian.