标题： 测试多点数值重整化群实频关联函数的抛物方程和U(1)规范恒等式 显示英文标题

标题： Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group

摘要： 最近，使用数值重整化群（NRG）的多点扩展（mpNRG），可以计算量子杂质模型的真实频率四点关联函数。 在本工作中，我们通过研究二点和四点函数之间的精确关系，对mpNRG的输出进行了多个数值一致性检查。 这包括贝特-萨利普方程和来自帕雷特形式主义的施温格-戴森方程，我们以两种形式相同但数值上不等价的方式进行了评估。 我们还研究了顶点和自能之间的第一阶U(1)王恒等式，这是我们首次在真实频率凯尔迪什形式主义中普遍推导出的。 我们通常发现所有关系之间有良好的一致，无论是在弱相互作用还是强相互作用下，往往达到百分之几的精度。 显示英文摘要

摘要： Recently, it has become possible to compute real-frequency four-point correlation functions of quantum impurity models using a multipoint extension of the numerical renormalization group (mpNRG). In this work, we perform several numerical consistency checks of the output of mpNRG by investigating exact relations between two- and four-point functions. This includes the Bethe-Salpeter equations and the Schwinger-Dyson equation from the parquet formalism, which we evaluate in two formally identical but numerically nonequivalent ways. We also study the first-order U(1) Ward identity between the vertex and the self-energy, which we derive for the first time in full generality in the real-frequency Keldysh formalism. We generally find good agreement of all relations, often up to a few percent, both at weak and at strong interaction.