标题： 解析延拓的平均谱方法：高效阻塞模式采样与离散化网格的依赖性 显示英文标题

标题： The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid

摘要： 平均谱方法是一种将虚时间或虚频率数据进行解析延拓到实轴的有前途的方法。它通过所有可接受的谱函数的泛函平均来确定噪声数据的解析延拓，这些谱函数的权重取决于它们与数据的拟合程度。其主要优点是明显没有可调节参数和平滑性约束，而是利用了数据中的统计噪声信息。其主要缺点是执行泛函积分的计算成本巨大。这里我们介绍了一种高效的实现方法，基于积分核的奇异值分解，消除了这一问题。它使我们能够详细分析平均谱方法的行为。我们发现，在表示谱函数的实频率网格上的离散化会偏差结果。网格点的分布起到默认模型的作用，而网格点的数量则起到正则化参数的作用。我们对此行为给出了定量解释，指出了默认模型的关键作用，并提供了一个选择它的实用方法，使平均谱方法成为一种可靠且高效的解析延拓技术。 显示英文摘要

摘要： The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible spectral functions, weighted by how well they fit the data. Its main advantage is the apparent lack of adjustable parameters and smoothness constraints, using instead the information on the statistical noise in the data. Its main disadvantage is the enormous computational cost of performing the functional integral. Here we introduce an efficient implementation, based on the singular value decomposition of the integral kernel, eliminating this problem. It allows us to analyze the behavior of the average spectrum method in detail. We find that the discretization of the real-frequency grid, on which the spectral function is represented, biases the results. The distribution of the grid points plays the role of a default model while the number of grid points acts as a regularization parameter. We give a quantitative explanation for this behavior, point out the crucial role of the default model and provide a practical method for choosing it, making the average spectrum method a reliable and efficient technique for analytic continuation.