标题： 一种改进的残差方案来计算动力学关联函数 显示英文标题

标题： A modified-residue prescription to calculate dynamical correlation functions

摘要： 使用数值方法解决多体问题的一个挑战是在极点上的多维积分。 通常需要将这些积分作为外部变量的函数进行评估。 一个例子是计算用于模拟响应函数的动力学关联函数，其中外部变量是频率。 标准的数值技术依赖于构建自适应网格，使用布里渊区内的特殊点或使用先进的展宽技术。 然而，大多数这些技术在网格较粗时会遇到困难。 在这里，我们提出，如果知道被积函数中的奇异性性质，就可以定义一个留数，并利用它来准确估计积分，并在网格较粗的情况下重现所有相应的奇异特征。 我们展示了该方法在不同场景下的有效性，包括计算具有不同奇异特征的关联函数、计算集体模态和态密度。 我们还提供了误差的定量分析，并表明该方法可以广泛适用。 显示英文摘要

摘要： One of the challenges in using numerical methods to address many-body problems is the multi-dimensional integration over poles. More often that not, one needs such integrations to be evaluated as a function of an external variable. An example would be calculating dynamical correlations functions that are used to model response functions, where the external variable is the frequency. The standard numerical techniques rely on building an adaptive mesh, using special points in the Brillouin zone or using advanced smearing techniques. Most of these techniques, however, suffer when the grid is coarse. Here we propose that, if one knows the nature of the singularity in the integrand, one can define a residue and use it to faithfully estimate the integral and reproduce all the resulting singular features even with a coarse grid. We demonstrate the effectiveness of the method for different scenarios of calculating correlation functions with different resulting singular features, for calculating collective modes and densities of states. We also present a quantitative analysis of the error and show that this method can be widely applicable.