One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which—regardless of its simplicity—is exactly solvable only in a few limiting cases and approximate many‐body methods are required for its solution. In this review, an overview on the non‐perturbative two‐particle self‐consistent method (TPSC), which was originally introduced to describe the electronic properties of the single‐band Hubbard model, is presented. A detailed derivation of the multi‐orbital generalization of TPSC is introduced here and particular features of the method on exemplary interacting models in comparison to dynamical mean‐field theory results are discussed.

中文翻译：

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多轨道哈伯模型的两粒子自洽方法

固态系统中最具挑战性的问题之一是电子相关性的微观分析。编码相关效应的最重要的最小模型是Hubbard Hamiltonian，尽管简单，但仅在少数情况下才是完全可解决的，并且需要采用多体方法进行求解。在这篇综述中，介绍了非扰动两粒子自洽方法（TPSC）的概述，该方法最初是用来描述单频带Hubbard模型的电子性质的。这里介绍了TPSC的多轨道泛化的详细推导，并讨论了与动态平均场理论结果相比，该方法在示例性交互模型上的特殊功能。