Ulybyshev Maksim, Assaad Fakher
Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany.
Würzburg-Dresden Cluster of Excellence ct.qmat, Am Hubland, 97074 Würzburg, Germany.
Phys Rev E. 2022 Aug;106(2-2):025318. doi: 10.1103/PhysRevE.106.025318.
We propose a method to mitigate heavy-tailed distributions in fermion quantum Monte Carlo simulations originating from zeros of the fermion determinant. In this case, the second moment of the observables might not be well defined, and we show that by merely changing the synchronization between local updates and computation of observables, one can reduce the prefactor of the heavy-tailed distribution, thus substantially suppressing statistical fluctuations of observables. We also show that the average, or the first moment, is well defined and hence is independent on our measuring scheme. The method is especially suitable for local observables similar to, e.g., double occupancy, where the resulting speedup can reach two orders of magnitude. For observables containing spatial correlators, the speedup is more moderate but still ranges between five and ten. Our results are independent on the nature of the auxiliary field, discrete or continuous, and pave the way to improve measurement strategies for hybrid Monte Carlo simulations.
我们提出了一种方法，以减轻费米子量子蒙特卡罗模拟中源自费米子行列式零点的重尾分布。在这种情况下，可观测量的二阶矩可能定义不明确，并且我们表明，仅通过改变局部更新与可观测量计算之间的同步，就可以降低重尾分布的前置因子，从而大幅抑制可观测量的统计波动。我们还表明，平均值或一阶矩定义明确，因此与我们的测量方案无关。该方法特别适用于类似于例如双重占据的局部可观测量，其加速比可达到两个数量级。对于包含空间关联函数的可观测量，加速比更为适中，但仍在五到十倍之间。我们的结果与辅助场的性质无关，无论是离散的还是连续的，并为改进混合蒙特卡罗模拟的测量策略铺平了道路。
