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 S0ex0ex=0ex0ex1/2 Heisenberg antiferromagnet at low temperature. We present results for both the transverse $(x)$ and longitudinal $(z)$ dynamic spin structure factors Sx,z(q,ω) at q0ex0ex=0ex0ex(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.