  We extend the Single Mode Approximation (SMA) into quantum Monte Carlo (QMC)
simulations to provides an efficient and fast method to obtain the dynamical
dispersion of quantum many-body systems. Based on Stochastic Series Expansion
(SSE) and its projector algorithms, The SMA + SSE method can simply extract the
dispersion of the dynamical spectrum in the long wave-length limit and the
upper bound of the dispersion elsewhere, without external calculations and high
technique barriers. Meanwhile, numerical analytic continuation methods require
the fine data of imaginary time correlations and complex programming.
Therefore, our method can approach the excitation dispersion of large systems,
e.g., we take the two-dimensional Heisenberg model on a $512 \times 512$ square
lattice. We demonstrate the effectiveness and efficiency of our method with
high precision via additional examples. We also demonstrate that SMA combined
with SSE goes beyond spin-wave theory with numerical results.
