Machine learning assisted derivation of effective low energy models for metallic magnets
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913789939548160 |
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| author | Sharma, Vikram Wang, Zhentao Batista, Cristian D. |
| author_facet | Sharma, Vikram Wang, Zhentao Batista, Cristian D. |
| contents | We consider the problem of extracting an effective low-energy spin model from a Kondo Lattice Model (KLM) with classical localized moments. The non-analytic dependence of the effective spin-spin interactions on the Kondo exchange $J$ excludes the possibility of using perturbation theory beyond the second order Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at zero temperature. Here we introduce a Machine Learning (ML) assisted protocol to extract effective two- and four-spin interactions by integrating out the conduction electrons of the original KLM. The resulting effective spin model reproduces the phase diagram obtained with the original KLM as a function of magnetic field and easy-axis anisotropy and reveals the effective four-spin interactions that are responsible for the field induced skyrmion crystal phase. Moreover, this minimal spin model enables an efficient computation of static and dynamical properties with a much lower numerical cost relative to the original KLM. A comparison of the dynamical spin structure factor in the fully polarized phase computed with the effective model and the original KLM reveals a good agreement for the magnon dispersion despite the fact that this information was not included in the training data set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09796 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Machine learning assisted derivation of effective low energy models for metallic magnets Sharma, Vikram Wang, Zhentao Batista, Cristian D. Strongly Correlated Electrons We consider the problem of extracting an effective low-energy spin model from a Kondo Lattice Model (KLM) with classical localized moments. The non-analytic dependence of the effective spin-spin interactions on the Kondo exchange $J$ excludes the possibility of using perturbation theory beyond the second order Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at zero temperature. Here we introduce a Machine Learning (ML) assisted protocol to extract effective two- and four-spin interactions by integrating out the conduction electrons of the original KLM. The resulting effective spin model reproduces the phase diagram obtained with the original KLM as a function of magnetic field and easy-axis anisotropy and reveals the effective four-spin interactions that are responsible for the field induced skyrmion crystal phase. Moreover, this minimal spin model enables an efficient computation of static and dynamical properties with a much lower numerical cost relative to the original KLM. A comparison of the dynamical spin structure factor in the fully polarized phase computed with the effective model and the original KLM reveals a good agreement for the magnon dispersion despite the fact that this information was not included in the training data set. |
| title | Machine learning assisted derivation of effective low energy models for metallic magnets |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2212.09796 |