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 Heisen berg antiferromagnet at low temperature. We present results for both the tr ansverse (x) and longitudinal (z) dynamic spin structure factors S-x,S-z(q, omega) at q = (pi ,0) 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) is 10% lower than at ( pi /2, pi /2). We also discuss the transverse and longitudinal multimagnon continua a nd their relevance to neutron scattering experiments.