Numerical renormalization group calculations for magnetic impurity systems with spin-orbit coupling and crystal-field effects

TL;DR

This paper introduces an extended and flexible version of the PointGroupNRG code that incorporates a wider range of symmetry groups, including all point and double groups, to improve NRG calculations for systems with complex crystal-field effects and spin-orbit coupling.

Contribution

The new code extends symmetry capabilities to all point and double groups and includes the full spin-orbital rotation group, enhancing NRG analysis of complex impurity systems.

Findings

Enhanced symmetry implementation in NRG code

Ability to handle complex impurity interactions

Improved accuracy and flexibility in calculations

Abstract

Exploiting symmetries in the numerical renormalization group (NRG) method significantly enhances performance by improving accuracy, increasing computational speed, and optimizing memory efficiency. Published codes focus on continuous rotations and unitary groups, which generally are not applicable to systems with strong crystal-field effects. The PointGroupNRG code implements symmetries related to discrete rotation groups, which are defined by the user in terms of Clebsch-Gordan coefficients, together with particle conservation and spin rotation symmetries. In this paper we present a new version of the code that extends the available finite groups, previously limited to simply reducible point groups, in a way that all point and double groups become accessible. It also includes the full spin-orbital rotation group. Moreover, to improve the code's flexibility for impurities with complex interactions, this new version allows to choose between a standard Anderson Hamiltonian for the impurity or, as another novel feature, an ionic model that requires only the spectrum and the impurity Lehmann amplitudes.