Elementary excitations for the two-dimensional quantum Heisenberg antiferromagnet

Abstract

The excitation spectrum of the antiferromagnetic spin-1/2 Heisenberg Hamiltonian H=tsumJS ${\mathrm{^}}_{\mathit{i}}$⋅S ${\mathrm{^}}_{\mathit{j}}$ on L×L lattices is evaluated by a projector quantum Monte Carlo method. These results suggest that the exact spectrum for the finite lattice is ${\mathrm{\omega }}_{\mathit{k}}$≃Z(L)${\mathrm{\omega }}_{\mathbf{k}}^{\mathrm{SW}}$, for all k, where ${\mathrm{\omega }}_{\mathbf{k}}^{\mathrm{SW}}$=4JS √1-${\gamma }_{\mathbf{k}}^2$ with ${\gamma }_{\mathbf{k}}$=(cos${\mathit{k}}_{\mathit{x}}$+cos${\mathit{k}}_{\mathit{y}}$)/2 is from linear-spin-wave theory. We find Z(L)=${\mathit{Z}}_{\mathit{E}}$+B/${\mathit{L}}^3$, leading to ${\mathit{Z}}_{\mathit{E}}$=1.21±0.03 for L=∞. A comparison with experiments on ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$ is discussed.