论文标题
将Tikhonov正则化连接到量子蒙特卡洛数据的分析延续的最大熵方法
Connecting Tikhonov regularization to the maximum entropy method for the analytic continuation of quantum Monte Carlo data
论文作者
论文摘要
分析延续是从量子蒙特卡洛（QMC）模拟中提取有关物理系统动力学特性的信息的重要步骤。已经提出了不同的分析延续方法，并且仍在开发中。本文探讨了一种基于在差异原理下重复应用Tikhonov正则化的正则化方法。该方法可以轻松地在任何线性代数软件包中实现，并且结果令人惊讶地接近最大熵方法（Maxent）。我们详细分析了该方法，并证明了它与Maxent的联系。此外，我们还提供了一种直接的方法来估计QMC数据的噪声水平，这对于差异原理的实际应用有助于当噪声水平可靠地可靠地知道时。
Analytic continuation is an essential step in extracting information about the dynamical properties of physical systems from quantum Monte Carlo (QMC) simulations. Different methods for analytic continuation have been proposed and are still being developed. This paper explores a regularization method based on the repeated application of Tikhonov regularization under the discrepancy principle. The method can be readily implemented in any linear algebra package and gives results surprisingly close to the maximum entropy method (MaxEnt). We analyze the method in detail and demonstrate its connection to MaxEnt. In addition, we provide a straightforward method for estimating the noise level of QMC data, which is helpful for practical applications of the discrepancy principle when the noise level is not known reliably.
