标题： IPT-DMFT的数学分析 显示英文标题

标题： A mathematical analysis of IPT-DMFT

摘要： 我们提供对动力平均场理论的数学分析，这是量子力学中一类称为嵌入方法的近似方法中的著名代表。 我们首先以教学和自包含的方式对有限Hubbard模型的动力平均场理论方程进行数学表述。 在回顾单体时间有序格林函数和自能的定义和性质，以及Hubbard和Anderson杂质模型的数学结构之后，我们描述了一个特定的杂质求解器，即迭代微扰理论求解器，该求解器可以方便地使用Matsubara的格林函数来表述。 在此框架下，我们在某些假设下证明动力平均场理论方程对于任何一组物理参数都存在解。 此外，我们建立了解的一些性质。 显示英文摘要

摘要： We provide a mathematical analysis of the Dynamical Mean-Field Theory, a celebrated representative of a class of approximations in quantum mechanics known as embedding methods. We start by a pedagogical and self-contained mathematical formulation of the Dynamical Mean-Field Theory equations for the finite Hubbard model. After recalling the definition and properties of one-body time-ordered Green's functions and self-energies, and the mathematical structure of the Hubbard and Anderson impurity models, we describe a specific impurity solver, namely the Iterated Perturbation Theory solver, which can be conveniently formulated using Matsubara's Green's functions. Within this framework, we prove under certain assumptions that the Dynamical Mean-Field Theory equations admit a solution for any set of physical parameters. Moreover, we establish some properties of the solution(s).