FINITE-SIZE STUDY OF THE GROUND-STATE ENERGY, SUSCEPTIBILITY, AND SPIN-WAVE VELOCITY FOR THE HEISENBERG-ANTIFERROMAGNET

The Green's-function Monte Carlo (GFMC) method is used to calculate very accurate ground-state energies of the two-dimensional, spin-1/2 Heisenberg antiferromagnet. The computations are performed on L x L square lattices up to L = 16 with varying uniform magnetization, which allows the extraction of the perpendicular susceptibility (chi) and spin-wave velocity (c). These two quantities are the lattice- or cutoff-dependent parameters that allow one to map the long-wavelength properties of the antiferromagnet onto the nonlinear sigma model and so are of general interest. Systematic errors present in previous GFMC calculations are addressed and corrected to yield results in excellent agreement with other numerical methods. I find, for the ground-state energy per site, -0.669 34(3); the susceptibility renormalization factor, Z(chi) = 0.535(5); and the spin-wave velocity renormalization factor, Z(c) = 1.10(3). Finite-size effects in the extraction of Z(c) and Z(chi) are discussed. The value of Z(chi) computed here is in agreement with the series-expansion results of Singh and of Zheng, Oitmaa, and Hamer, thereby clearing up a previous inconsistency between the series-expansion and quantum Monte Carlo predictions.