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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.15260 |
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| _version_ | 1866916159935217664 |
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| author | Azor, Miguel Escobar Alrakik, Amer de Bentzmann, Louan Telleria-Allika, Xabier de Merás, Alfredo Sánchez Evangelisti, Stefano Berger, J. Arjan |
| author_facet | Azor, Miguel Escobar Alrakik, Amer de Bentzmann, Louan Telleria-Allika, Xabier de Merás, Alfredo Sánchez Evangelisti, Stefano Berger, J. Arjan |
| contents | At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localisation in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localise are made. The density profiles we obtain emerge naturally when we minimise the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure which has been predicted to be ground-state structure of the two-dimensional Wigner crystal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15260 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments Azor, Miguel Escobar Alrakik, Amer de Bentzmann, Louan Telleria-Allika, Xabier de Merás, Alfredo Sánchez Evangelisti, Stefano Berger, J. Arjan Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localisation in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localise are made. The density profiles we obtain emerge naturally when we minimise the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure which has been predicted to be ground-state structure of the two-dimensional Wigner crystal. |
| title | The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2309.15260 |