The PointGroupNRG code for numerical renormalization group calculations with discrete point-group symmetries

TL;DR

This paper introduces PointGroupNRG, a Julia-based numerical renormalization group code that efficiently incorporates discrete point-group symmetries for impurity models, enhancing computational accuracy and performance.

Contribution

The authors developed a novel NRG code implementing discrete point-group symmetries, specifically for impurity systems with crystal field effects, which was not previously available.

Findings

Demonstrated the code's effectiveness on a two-impurity RKKY model.

Showed performance improvements by exploiting orbital symmetries.

Validated the accuracy of symmetry implementation through benchmark results.

Abstract

The numerical renormalization group (NRG) has been widely used as a magnetic impurity solver since the pioneering works by Wilson. Over the past decades, a significant attention has been focused on the application of symmetries in order to reduce the computational cost of the calculations and to improve their accuracy. In particular, a notable progress has been made in implementing continuous symmetries such as $SO(3)$, useful for studying impurities in an isotropic medium, or $SU(N)$, which is applicable to a wide range of systems. In this work, we focus on the application of discrete point group symmetries, which are particularly relevant for impurity systems in metals where crystal field effects are important. With this aim, we have developed an original NRG code written in the Julia language, PointGroupNRG, where we have implemented crystal point-group symmetries for the Anderson impurity model, as well as the continuous spin and charge symmetries. Among other results, we demonstrate the advantage of our procedure by applying the code to a two-impurity model with RKKY interaction and an impurity system with two orbitals of $E_g$ symmetry and two channels. We also provide benchmarks to show the performance improvements obtained by exploiting the orbital symmetries.