Developing numerical RG beyond its current limitations

Abstract:
Quantum dot (QD) devices can nowadays be routinely prepared in Coulomb blockade and thus exhibit the famous Kondo effect when metallic leads are attached. While it originally posed an insurmountable obstacle, the seminal works of K. G. Wilson on the application of the numerical renormalization group (NRG) techniques to the single impurity Anderson model (SIAM) brought a final solution [1,2]. The, NRG approach has then been further refined and  extended to incorporate superconducting correlations in the leads. Nevertheless, while the experimental advances allow for more complex QD devices, NRG has still several limits in regards to the number of QDs, the presence of an insulator gap in the lead  and the number of superconducting leads. The later two can, however, be lifted by two newly developed approaches discussed in this talk [3].

The first is herein referred to as the log-gap NRG approach and the other as the sigma-additive NRG approach. The first allows to solve for problems with insulator leads, where the presence of the spectral gap is expected to compete with the ordinary Kondo effect. First ever results on SIAM with a spectral gap can be thus shown. The log-gap approach is also applicable to the two-lead superconducting Anderson model. Together with the sigma-additive approach, it is then benchmarked against the standard NRG techniques. The sigma-additive approach however offers generalizations ti implement  additional superconducting leads.

[1] H. R. Krishna-murthy, J. W. Wilkins, and K. G. Wilson, Phys. Rev. B 21, 1003 (1980).
[2] H. R. Krishna-murthy, J. W. Wilkins, and K. G. Wilson, Phys. Rev. B 21, 1044 (1980).
[3] P. Zalom and M. Žonda, Phys. Rev. B 105, 205412 (2022).