标题： 重整化微扰理论中安德森杂质模型的高阶项 显示英文标题

标题： High-order terms in the renormalized perturbation theory for the Anderson impurity model

摘要： 我们研究单杂质安德森模型的重整化微扰理论，特别是自能在重整化耦合$\tilde{U}$的幂级数展开中的高阶项。 尽管重整化理论中存在抵消项，可能会使图示学显得复杂，但我们展示了如何通过按骨架图顺序进行计算来无缝地处理这些项。 我们描述了与重整化自能和四顶点相关的图示如何自动生成、转换为积分并进行数值积分。 为了提高我们方法的效率，我们引入了一个广义的$k$-粒子/空穴传播子，用于解析简化结果积分并降低积分的维度。 我们给出了自能和谱密度在$\tilde{U}$的第五阶的结果，针对模型不对称性的不同值，并将其与数值重整化群计算进行比较。 显示英文摘要

摘要： We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling $\tilde{U}$. Though the presence of counter-terms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four-vertex can be automatically generated, translated into integrals and numerically integrated. To maximize the efficiency of our approach we introduce a generalized $k$-particle/hole propagator, which is used to analytically simplify the resultant integrals and reduce the dimensionality of the integration. We present results for the self-energy and spectral density to fifth order in $\tilde{U}$, for various values of the model asymmetry, and compare them to a Numerical Renormalization Group calculation.