交错数值重整化群作为一种有效的多带杂质解算器
Interleaved numerical renormalization group as an efficient multiband impurity solver
摘要：
量子杂质问题可以使用数值重整化群（NRG）来解决，它涉及到离散的自由传导电子系统和映射到一个“威尔逊链”。最近表明，不同电子物种的Wilson链可以通过使用修改的离散化来交织，从而显著提高RG方案的数值效率[Phys.Rev.B89，121105（R）（2014）]。在这里，我们系统地研究的准确性和效率的“交错”NRG（iNRG）方法的上下文中的单个杂质安德森模型，双通道近藤模型，和三通道安德森-洪德模型。iNRG的性能是明确的比较与“标准”NRG（sNRG）：当保持每次迭代的状态的平均数量是相同的，在这两个计算中，iNRG的准确性是等同于sNRG，但计算成本显着降低iNRG时，利用相同的对称性。虽然iNRG弱破坏SU（N）通道对称性（如果存在），但精度和数值成本完全可以与利用完全对称性的sNRG竞争。因此，iNRG被证明是一个可行的和技术上简单的替代sNRG的高对称性模型。此外，iNRG可用于解决sNRG无法解决的一系列较低对称性的多频带问题。
英文摘要：
Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a `Wilson chain'. It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014)]. Here we systematically examine the accuracy and efficiency of the `interleaved' NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with `standard' NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are signifficantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.
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