  We extend the Single Mode Approximation (SMA) into quantum Monte Carlo (QMC)
versions to obtain the dynamical dispersion of quantum many-body systems. Based
on Stochastic Series Expansion (SSE) and its projector algorithms, we put
forward the ways to realize the calculation of SMA within the SSE frame. The
SMA + QMC method can quickly extract the dispersion of the dynamical spectrum
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 spectrum of large systems, e.g., we take a $512 \times 512$ spin
model as an example in this work. We demonstrate the effectiveness and
efficiency of our method with high precision via several examples.

Strongly Correlated Electrons