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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2307.03658 |
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| _version_ | 1866912073918709760 |
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| author | Calvo-Fernández, Aitor Blanco-Rey, María Eiguren, Asier |
| author_facet | Calvo-Fernández, Aitor Blanco-Rey, María Eiguren, Asier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03658 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The PointGroupNRG code for numerical renormalization group calculations with discrete point-group symmetries Calvo-Fernández, Aitor Blanco-Rey, María Eiguren, Asier Strongly Correlated Electrons 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. |
| title | The PointGroupNRG code for numerical renormalization group calculations with discrete point-group symmetries |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2307.03658 |