Ground-state and low-lying excitations of the Heisenberg antiferromagnet

Monte Carlo methods are used to determine the exact ground-state energy of the spin-(1/2 Heisenberg antiferromagnet on two-dimensional square periodic lattices up to size 32×32. The extrapolated ground-state energy for infinite lattice size is -0.334 59±0.000 05. In addition, splittings between the ground state and the lowest spin-1 and -2 excitations are determined as a function of lattice size. The scaling of both the ground-state energy and the gap are in agreement with that predicted by spin-wave theory over a wide range of lattice sizes. In particular, numerical results demonstrate convincingly the lack of a gap for infinite systems, and that the gap for finite systems scales with the inverse volume of the lattice. Finally, we present results for the ground-state spin-correlation function. Our approximate results for larger lattices indicate that the staggered magnetization is 0.34±0.01 units where the saturated value is (1/2.