High-Energy Magnon Dispersion and Multimagnon Continuum in the Two-Dimensional Heisenberg Antiferromagnet

We use quantum Monte Carlo simulations and numerical analytic continuation to study high-energy spin excitations in the two-dimensional $S=1\mathrm{}/2$ Heisenberg antiferromagnet at low temperature. We present results for both the transverse $\left(x\right)$ and longitudinal $\left(z\right)$ dynamic spin structure factors $S_{x,z}(\mathbf{q},\omega )$ at $\mathbf{q}=(\pi ,0\mathrm{})$ and $(\pi /2,\pi /2)$. Linear spin-wave theory predicts no dispersion on the line connecting these momenta. Our calculations show that in fact the magnon energy at $(\pi ,0\mathrm{})$ is $10\%$ lower than at $(\pi /2,\pi /2)$. We also discuss the transverse and longitudinal multimagnon continua and their relevance to neutron scattering experiments.