Monte Carlo study of the S=1/2 and S=1 Heisenberg antiferromagnet on a spatially anisotropic square lattice

We present a quantum Monte Carlo study of a Heisenberg antiferromagnet on a spatially anisotropic square lattice, where the coupling strength in the x direction (J(x)) is different from that in the y direction (J(y)). By varying the anisotropy alpha from 0 to 1, we interpolate between the one-dimensional chain and the two-dimensional isotropic square lattice. Both S=1/2 and S=1 systems are considered separately in order to facilitate comparison. The temperature dependence of the uniform susceptibility and the spin-spin correlation length are computed down to very low temperatures for various values of alpha. For S=1, the existence of a quantum critical point at alpha(c)(S=1)=0.040(5) as well as the scaling of the spin gap is confirmed. Universal quantities predicted from the O(3) nonlinear sigma model agree with our results at alpha=0.04 without any adjustable parameters. On the other hand, the S=1/2 results are consistent with alpha(c)(S=1/2)=0, as discussed by a number of previous theoretical studies. Experimental implications for S=1/2 compounds such as Sr2CuO3 are also discussed.