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 $\alpha^{S=1}_c=0.040(5)$ as well as the scaling of the spin gap is confirmed. Universal quantities predicted from the ${\cal O}(3)$ 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 $\alpha^{S=1/2}_c=0$, as discussed by a number of previous theoretical studies. Experimental implications for $S=1/2$ compounds such as Sr$_2$CuO$_3$ are also discussed.