论文标题
扩展平均频谱方法：网格点采样和密度平均
Extending the average spectrum method: Grid points sampling and density averaging
论文作者
论文摘要
将假想时间或频率数据与真实轴的分析延续是从量子蒙特卡洛模拟中提取动力学特性的关键步骤。平均光谱方法通过在所有非阴性光谱上集成了由它们的数据符合程度来加权的所有非负光谱，从而提供了优雅的解决方案。在最近的一篇论文中，我们发现像Feynman的路径综合群中的功能积分不可或缺，没有明确的连续体限制。取而代之的是，极限取决于离散的网格，其选择可能会强烈偏向结果。在本文中，我们证明了对网格点进行采样，而不是保持固定，还会改变功能积分极限，而是有助于极大地克服偏见。我们提供了一种有效的算法来进行采样，并显示网格点的密度如何作为默认模型，具有显着降低的偏置效果。其余的偏置主要取决于网格密度的宽度，因此我们向前一步，平均也超过了不同宽度的密度。对于某些类别的密度，包括高斯和指数的密度，可以在分析上进行此宽度平均，从而消除了在不引入任何计算开销的情况下指定此参数的需求。
Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating over all non-negative spectra weighted by how well they fit the data. In a recent paper, we found that discretizing the functional integral as in Feynman's path-integrals, does not have a well-defined continuum limit. Instead, the limit depends on the discretization grid whose choice may strongly bias the results. In this paper, we demonstrate that sampling the grid points, instead of keeping them fixed, also changes the functional integral limit and rather helps to overcome the bias considerably. We provide an efficient algorithm for doing the sampling and show how the density of the grid points acts now as a default model with a significantly reduced biasing effect. The remaining bias depends mainly on the width of the grid density, so we go one step further and average also over densities of different widths. For a certain class of densities, including Gaussian and exponential ones, this width averaging can be done analytically, eliminating the need to specify this parameter without introducing any computational overhead.
