Finite-size scaling of the ground-state parameters of the two-dimensional Heisenberg model

The ground-state parameters of the two-dimensional S=1/2 antiferromagnetic Heisenberg model are calculated using the stochastic series expansion quantum Monte Carlo method for L×L lattices with L up to 16. The finite-size results for the energy E, the sublattice magnetization M, the long-wavelength susceptibility χ_⊥(q=2π/L), and the spin stiffness ρ_s, are extrapolated to the thermodynamic limit using fits to polynomials in 1/L, constrained by scaling forms previously obtained from renormalization-group calculations for the nonlinear σ model and chiral perturbation theory. The results are fully consistent with the predicted leading finite-size corrections, and are of sufficient accuracy for extracting also subleading terms. The subleading energy correction (∼1/L⁴) agrees with chiral perturbation theory to within a statistical error of a few percent, thus providing numerical confirmation of the finite-size scaling forms to this order. The extrapolated ground- state energy per spin is E=-0.669437(5). The result from previous Green’s function Monte Carlo (GFMC) calculations is slightly higher than this value, most likely due to a small systematic error originating from “population control” bias in GFMC. The other extrapolated parameters are M=0.3070(3), ρ_s=0.175(2), χ_⊥=0.0625(9), and the spin-wave velocity c=1.673(7). The statistical errors are comparable with those of previous estimates obtained by fitting loop algorithm quantum Monte Carlo data to finite-temperature scaling forms. Both M and ρ_s obtained from the finite-T data are, however, a few error bars higher than the present estimates. It is argued that the T=0 extrapolations performed here are less sensitive to effects of neglected higher-order corrections, and therefore should be more reliable.