Phase Diagram of S= 1/2 Antiferromagnetic Heisenberg Model on a Dimerized Square Lattice

The ground state energy, the energy gap and the Fourier transform of the staggered spin correlation function S(Q) at zero temperature are investigated for the 5=1/2 antiferromagnetic Heisenberg model on a dimerized square lattice with the help of the spin-wave approximations, the second-order perturbation expansion and the quantum Monte Carlo simulations. In contrast to one-dimensional case, the spin gap appears above a finite critical value of the dimerization parameter. Sc - 0.303, where the second-order transition takes place. The antiferromagnetic long range order exists below Sc. The critical exponent of the order parameter in the antiferromagnetically ordered state is estimated by quantum Monte Carlo calculation to be -{dc∼- with B=0.27 ±0.04, while the correlation length in the spin gap region is scaled as - (S-Sc)v with v= 1.36±0.05. All of them are different from the estimates in one-dimension, v=l and the spin-wave approximation, fi=v=l. Possible relevance of our result for the spin gap behavior in high-Tc superconductors is also discussed.