Affiliation
University of the Basque Country (UPV-EHU)
Donostia International Physics Center (DIPC)
Talk Title
The numerical renormalization group with discrete rotation symmetries: a tool to study crystal field effects in magnetic impurity systems
Abstract
The numerical renormalization group (NRG) has been widely used as a magnetic impurity solver since the pioneering works by Wilson [1]. An important line of research in this field has been the explicit application of symmetries in order to reduce the computational cost of the calculations and to improve their accuracy. Notable progress has been made in implementing continuous symmetries such as SO(3), useful for studying impurities in an isotropic medium, or SU(N) with $N>2$, which is realized in some specific materials and in quantum dot systems [2]. In our work, we focus on the application of discrete point group symmetries, an approach that is relevant for impurity systems in metals where crystal field effects are important [3]. With this aim, we have developed our own NRG code in Julia language [4], where we have implemented crystal symmetries for the Anderson impurity model. We use this tool to study phases and fixed points of NRG flow for impurity systems embedded in crystal fields, and we focus on the comparison with their better-known counterparts with full (continuous) rotational symmetry. We demonstrate that calculations with multiple orbitals and channels in the framework of real metallic systems can be efficiently carried out taking advantage of the discrete symmetries.
[1] K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975).
[2] R. Bulla, T.A. Costi, and T. Pruschke, Rev. Mod. Phys. 80, 395 (2008).
[3] Ph. Nozières and A. Blandin, J. Physique 41, 193 (1980).
[4] https://julialang.org