Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
| dc.creator | Sandvik, A. W. | |
| dc.date | 1997-07-11 | |
| dc.date.accessioned | 2026-07-07T12:16:41Z | |
| dc.date.available | 2026-07-07T12:16:41Z | |
| dc.description | 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 | |
| dc.description | 16 pages, RevTex, 9 PostScript figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9707123 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9707123 | |
| dc.identifier | Phys.Rev.B56:11678,1997 | |
| dc.identifier | doi:10.1103/PhysRevB.56.11678 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/211880 | |
| dc.subject | Strongly Correlated Electrons | |
| dc.subject | High Energy Physics - Lattice | |
| dc.title | Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model | |
| dc.type | text |