Bayesian Inference and the Analytic Continuation of Imaginary-Time Quantum Monte Carlo Data
Bayesian Inference and the Analytic Continuation of Imaginary-Time Quantum Monte Carlo Data
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DOI：
10.1007/978-94-011-5430-7_19
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发表时间：
1995-12
期刊：
影响因子：
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通讯作者：
J. Gubernatis;J. Bonca;M. Jarrell
中科院分区：
文献类型：
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作者：
J. Gubernatis;J. Bonca;M. Jarrell
我们提出了一种使用贝叶斯统计推断和最大熵原理来分析连续虚时间量子蒙特卡罗数据的方法。我们提供了开创性文献中缺乏的细节，但对于有动力的读者理解这些方法中所体现的假设和近似值来说非常重要。首先，我们总结了量子相关函数与谱密度之间的一般关系。然后，我们回顾贝叶斯推理的基本原理、形式主义和哲学，并讨论该方法在分析连续问题中的应用。接下来，我们将介绍对称、无限维安德森哈密顿量的详细案例研究。我们选择这个哈密顿量是因为它的谱密度的定性特征已经很好地确定，并且因为存在一种特别方便的算法来产生虚时间格林函数数据。显示的是数据和解决方案鉴定的所有中间步骤。在此示例的上下文中讨论了分析延续中仔细的数据准备和错误传播的重要性。然后，我们回顾这些或相关程序所应用的不同物理系统和物理量。最后，我们描述了有关我们的方法的应用的其他特征、它们可能的改进以及需要进一步研究的领域。
We present a way to use Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time quantum Monte Carlo data. We supply the details that are lacking in the seminal literature but are important for the motivated reader to understand the assumptions and approximations embodied in these methods. First, we summarize the general relations between quantum correlation functions and spectral densities. We then review the basic principles, formalism, and philosophy of Bayesian inference and discuss the application of this approach in the context of the analytic continuation problem. Next, we present a detailed case study for the symmetric, infinite-dimension Anderson Hamiltonian. We chose this Hamiltonian because the qualitative features of its spectral density are well established and because a particularly convenient algorithm exists to produce the imaginary-time Green's function data. Shown are all the intermediate steps of data and solution qualification. The importance of careful data preparation and error propagation in the analytic continuation is discussed in the context of this example. Then, we review the different physical systems and physical quantities to which these, or related, procedures have been applied. Finally, we describe other features concerning the application of our methods, their possible improvement, and areas for additional study.