Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice

The S = 1/2 and S = 1 two-dimensional quantum Heisenberg anti ferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the cot-relation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works, It is confirmed that the quantum critical phenomena on (lie phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S = 1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.