Two-dimensional Heisenberg antiferromagnet: A numerical study

Abstract

We describe a numerical simulation of the isotropic spin-½ Heisenberg antiferromagnet on square lattices of size 4×4, 6×6, and 8×8. A Hamiltonian Monte Carlo method is used to measure the energies of the lowest-lying singlet and triplet states, and we extrapolate these results to give estimates of the properties of large antiferromagnets. Our result for the ground-state energy per spin is $\frac{E_0}{N^2}=-0.672\mathrm{}\pm 0.001$ for an infinite system. Within our statistical accuracy, the singlet-triplet gap behaves as $E_1-E_0\approx \frac{2.1}{N}$, which implies that the infinite system is gapless.