Phase Diagram of S=1/2 Quasi-One-Dimensional Heisenberg Model with Dimerized Antiferromagnetic Exchange

The quantum phase transition between a spin gap state and an antiferromagnetic phase is investigated. We study S=1/2 antiferromagnetic Heisenberg chains coupled by antiferromagnetic interchain interaction. The intrachain exchanges have alternating strength. The phase boundary between the antiferromagnetically ordered phase and a spin gap phase is also obtained in a parameter space of the amplitude of the interchain coupling and the dimerization. The spin-wave approximation substantially overestimates the antiferromagnetic phase. The competition between the long range order and the spin gap is examined in detail. We estimate a variety of critical exponents at the transition, namely, exponents v, θ and z defined as the exponent of the correlation length, the magnetization curve and the dynamical exponent, respectively. From the quantum Monte Carlo simulation, the exponents v, θ and z are estimated to be unity. The exponents v and θ are different from the estimated values in one dimension. It suggests that the universality changes due to the dimensionality change. In our estimates, the exponent v does not agree with the prediction from three dimensional classical Heisenberg model. We also discuss the relevance of our result to spin-Peierls systems with lattice distortion.