Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model

TL;DR

This paper uses quantum Monte Carlo simulations to accurately determine the ground state parameters of the 2D Heisenberg model, confirming finite-size scaling predictions and providing the most precise estimates to date.

Contribution

It presents the first numerical confirmation of subleading finite-size corrections in the 2D Heisenberg model and achieves the most accurate ground state energy estimate.

Findings

Ground state energy per spin: -0.669437(5)

Sublattice magnetization: 0.3070(3)

Spin stiffness: 0.175(2)

Abstract

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 chi_perp(q=2*pi/L), and the spin stiffness rho_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 sigma 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 (proportional to 1/L^4) agrees with chiral perturbation theory to within a statistical error of a few percent, thus providing the first numerical confirmation of the finite-size scaling forms to this order. The extrapolated ground state energy per spin, E=-0.669437(5), is the most accurate estimate reported to date. The most accurate Green's function Monte Carlo (GFMC) result 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), rho_s = 0.175(2), chi_perp = 0.0625(9), and the spinwave velocity c=1.673(7). The statistical errors are comparable with those of the best previous estimates, obtained by fitting loop algorithm quantum Monte Carlo data to finite-temperature scaling forms. Both M and rho_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