We present a new estimator for the self-energy based on a combination of two equations of motion and discuss its benefits for numerical renormalization group (NRG) calculations. In challenging regimes, NRG results from the standard estimator, a ratio of two correlators, often suffer from artifacts: The imaginary part of the retarded self-energy is not properly normalized and, at low energies, overshoots to unphysical values and displays wiggles. We show that the new estimator resolves the artifacts in these properties as they can be determined directly from the imaginary parts of auxiliary correlators and do not involve real parts obtained by Kramers–Kronig transform. Furthermore, we find that the new estimator yields converged results with reduced numerical effort (for a lower number of kept states) and thus is highly valuable when applying NRG to multiorbital systems. Our analysis is targeted at NRG treatments of quantum impurity models, especially those arising within dynamical mean-field theory, but most results can be straightforwardly generalized to other impurity or cluster solvers.

中文翻译：

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自能数值重整化群计算的改进估计器

我们基于两个运动方程的组合提出了一种新的自能估计器，并讨论了它对数值重整化群 (NRG) 计算的好处。在具有挑战性的情况下，NRG 由标准估计量（两个相关器的比率）产生，经常受到伪影的影响：延迟的自能的虚部未正确归一化，并且在低能量下，超调到非物理值并显示摆动。我们表明，新的估计器解决了这些属性中的伪影，因为它们可以直接从辅助相关器的虚部确定，而不涉及通过 Kramers-Kronig 变换获得的实部。此外，我们发现新的估计器在减少数值工作量的情况下产生收敛结果（对于较少数量的保持状态），因此在将 NRG 应用于多轨道系统时非常有价值。我们的分析针对量子杂质模型的 NRG 处理，尤其是动态平均场理论中出现的那些，但大多数结果可以直接推广到其他杂质或簇求解器。