Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations

We extend the single-mode Approximation (SMA) into quantum Monte Carlo 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 dispersion 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. We further illustrate that SMA is able to extract useful information in strongly correlated systems with competing states.