Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations
Abstract Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant challenge. In this work, we introduce a framework f...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | Communications Physics |
| Online Access: | https://doi.org/10.1038/s42005-025-01955-z |
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| _version_ | 1832571589763268608 |
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| author | Imelda Romero Jannes Nys Giuseppe Carleo |
| author_facet | Imelda Romero Jannes Nys Giuseppe Carleo |
| author_sort | Imelda Romero |
| collection | DOAJ |
| description | Abstract Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant challenge. In this work, we introduce a framework for embedding lattice symmetries in fermionic wavefunctions and demonstrate its ability to target both ground states and low-lying excitations. Using group-equivariant neural backflow transformations, we study the t-V model on a square lattice away from half-filling. Our symmetry-aware backflow significantly improves ground-state energies and yields accurate low-energy excitations for lattices up to 10 × 10. We also compute accurate two-point density-correlation functions and the structure factor to identify phase transitions and critical points. These findings introduce a symmetry-aware framework important for studying quantum materials and phase transitions. |
| format | Article |
| id | doaj-art-712a0f11ee2c493ebe6de06f015dcfde |
| institution | Kabale University |
| issn | 2399-3650 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Communications Physics |
| spelling | doaj-art-712a0f11ee2c493ebe6de06f015dcfde2025-02-02T12:28:03ZengNature PortfolioCommunications Physics2399-36502025-01-018111010.1038/s42005-025-01955-zSpectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformationsImelda Romero0Jannes Nys1Giuseppe Carleo2Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Abstract Neural networks have shown to be a powerful tool to represent the ground state of quantum many-body systems, including fermionic systems. However, efficiently integrating lattice symmetries into neural representations remains a significant challenge. In this work, we introduce a framework for embedding lattice symmetries in fermionic wavefunctions and demonstrate its ability to target both ground states and low-lying excitations. Using group-equivariant neural backflow transformations, we study the t-V model on a square lattice away from half-filling. Our symmetry-aware backflow significantly improves ground-state energies and yields accurate low-energy excitations for lattices up to 10 × 10. We also compute accurate two-point density-correlation functions and the structure factor to identify phase transitions and critical points. These findings introduce a symmetry-aware framework important for studying quantum materials and phase transitions.https://doi.org/10.1038/s42005-025-01955-z |
| spellingShingle | Imelda Romero Jannes Nys Giuseppe Carleo Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations Communications Physics |
| title | Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations |
| title_full | Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations |
| title_fullStr | Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations |
| title_full_unstemmed | Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations |
| title_short | Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations |
| title_sort | spectroscopy of two dimensional interacting lattice electrons using symmetry aware neural backflow transformations |
| url | https://doi.org/10.1038/s42005-025-01955-z |
| work_keys_str_mv | AT imeldaromero spectroscopyoftwodimensionalinteractinglatticeelectronsusingsymmetryawareneuralbackflowtransformations AT jannesnys spectroscopyoftwodimensionalinteractinglatticeelectronsusingsymmetryawareneuralbackflowtransformations AT giuseppecarleo spectroscopyoftwodimensionalinteractinglatticeelectronsusingsymmetryawareneuralbackflowtransformations |