标题： 二维加速HMC的降采样映射 显示英文标题

标题： Decimation map in 2D for accelerating HMC

摘要： 为了加速分子动力学蒙特卡洛（HMC）算法中的场变换，我们考虑了简化映射的一种变体——降采样映射，该映射可以被视为一种粗粒化变换。 使用二维纯规范模型$U(1)$，结合引导蒙特卡洛算法，我们展示了拓扑电荷的综合自相关时间可以在壁钟时间内实现指数级改进。 我们的研究表明，在大$\beta$的情况下，引入重整化群图是一种强大且必不可少的加速HMC算法的要素。 显示英文摘要

摘要： To accelerate the HMC with field transformation, we consider a variant of the trivializing map, the decimation map, which can be regarded as a coarse-graining transformation. Using the 2D $U(1)$ pure gauge model, combined with the guided Monte Carlo algorithm, we show that the integrated autocorrelation time of the topological charge can be exponentially improved in the wall clock time. Our study indicates that incorporating renormalization group picture is a powerful and essential ingredient to accelerate the HMC at large $\beta$.