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 = 1/2 Heisenberg antiferromagnet at low temperature. We present results for both the transverse \(x\) and longitudinal \(z\) dynamic spin structure factors S_x,z\(q,ω\) at q = \(π,0\) and \(π/2,π/2\). Linear spin-wave theory predicts no dispersion on the line connecting these momenta. Our calculations show that in fact the magnon energy at \(π,0\) is 10% lower than at \(π/2,π/2\). We also discuss the transverse and longitudinal multimagnon continua and their relevance to neutron scattering experiments.