Interleaved numerical renormalization group as an efficient multiband impurity solver

TL;DR

The paper introduces an interleaved NRG method that enhances computational efficiency for multiband quantum impurity problems while maintaining accuracy comparable to standard NRG, especially in high-symmetry models.

Contribution

The study systematically evaluates the accuracy and efficiency of interleaved NRG (iNRG) compared to standard NRG (sNRG), demonstrating iNRG's advantages in computational cost and applicability to lower-symmetry models.

Findings

iNRG achieves accuracy comparable to sNRG at similar state retention levels.

iNRG significantly reduces computational costs relative to sNRG when exploiting the same symmetries.

iNRG is effective for high-symmetry models and extends to lower-symmetry multiband problems.

Abstract

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.