Two-dimensional spin-1/2 Heisenberg antiferromagnet: A quantum Monte Carlo study.

Abstract

Spin-1/2 nearest-neighbor Heisenberg antiferromagnet on a square lattice is studied via a large-scale quantum Monte Carlo simulation. We developed a fast and efficient multispin coding algorithm on a parallel supercomputer, based on the Suzuki-Trotter transformation. We performed high-statistics simulations on lattices as large as 128\ifmmode\times\else\texttimes\fi{}128 spins, in the temperature range from 0.25J to 2.5J. We calculated energy, specific heat, uniform and staggered susceptibility, and staggered correlation function, from which we deduce the correlation length. For temperatures higher than J, the results are in excellent agreement with high-temperature series expansion. At low temperatures the long-wavelength behavior is essentially classical. Our data show that the correlation length and staggered susceptibility are quantitatively well described by the renormalized classical picture at the two-loop level of approximation. From the divergence of correlation length, we deduce the value of quantum-renormalized spin stiffness, ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$/J=0.199(2). We give evidence that the correlation function is of Ornstein-Zernike type. By comparing the largest measured correlation lengths with neutron scattering experiments on ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$, we deduce the value of effective exchange coupling J=1450\ifmmode\pm\else\textpm\fi{}30 K.