Simple Fermionic backflow states via a systematically improvable tensor decomposition
Abstract Strongly correlated electrons give rise to an array of electronic properties increasingly exploited in many emerging materials and molecular processes. However, the reliable numerical simulation of this quantum many-body problem still poses an outstanding challenge, in particular when accou...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2025-04-01
|
| Series: | Communications Physics |
| Online Access: | https://doi.org/10.1038/s42005-025-02083-4 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850181437887610880 |
|---|---|
| author | Massimo Bortone Yannic Rath George H. Booth |
| author_facet | Massimo Bortone Yannic Rath George H. Booth |
| author_sort | Massimo Bortone |
| collection | DOAJ |
| description | Abstract Strongly correlated electrons give rise to an array of electronic properties increasingly exploited in many emerging materials and molecular processes. However, the reliable numerical simulation of this quantum many-body problem still poses an outstanding challenge, in particular when accounting for the fermionic statistics of electrons. In this work, we introduce a compact and systematically improvable fermionic wave function based on a CANDECOMP/PARAFAC (CP) tensor decomposition of backflow correlations in second quantization. This ansatz naturally encodes many-electron correlations without the ordering dependence of other tensor decompositions. We benchmark its performance against standard models, demonstrating improved accuracy over comparable methods in Fermi-Hubbard and molecular systems and competitive results with state-of-the-art density matrix renormalization group (DMRG) in ab initio 2D hydrogenic lattices. By considering controllable truncations in the rank and range of the backflow correlations, as well as screening the local energy contributions for realistic Coulomb interactions, we obtain a scalable and interpretable approach to strongly correlated electronic structure problems that bridges tensor factorizations and machine learning-based representations. |
| format | Article |
| id | doaj-art-e977cd246bb04cdfb7cf58e059bda79b |
| institution | OA Journals |
| issn | 2399-3650 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Communications Physics |
| spelling | doaj-art-e977cd246bb04cdfb7cf58e059bda79b2025-08-20T02:17:54ZengNature PortfolioCommunications Physics2399-36502025-04-018111310.1038/s42005-025-02083-4Simple Fermionic backflow states via a systematically improvable tensor decompositionMassimo Bortone0Yannic Rath1George H. Booth2Department of Physics and Thomas Young Centre, King’s College London, StrandDepartment of Physics and Thomas Young Centre, King’s College London, StrandDepartment of Physics and Thomas Young Centre, King’s College London, StrandAbstract Strongly correlated electrons give rise to an array of electronic properties increasingly exploited in many emerging materials and molecular processes. However, the reliable numerical simulation of this quantum many-body problem still poses an outstanding challenge, in particular when accounting for the fermionic statistics of electrons. In this work, we introduce a compact and systematically improvable fermionic wave function based on a CANDECOMP/PARAFAC (CP) tensor decomposition of backflow correlations in second quantization. This ansatz naturally encodes many-electron correlations without the ordering dependence of other tensor decompositions. We benchmark its performance against standard models, demonstrating improved accuracy over comparable methods in Fermi-Hubbard and molecular systems and competitive results with state-of-the-art density matrix renormalization group (DMRG) in ab initio 2D hydrogenic lattices. By considering controllable truncations in the rank and range of the backflow correlations, as well as screening the local energy contributions for realistic Coulomb interactions, we obtain a scalable and interpretable approach to strongly correlated electronic structure problems that bridges tensor factorizations and machine learning-based representations.https://doi.org/10.1038/s42005-025-02083-4 |
| spellingShingle | Massimo Bortone Yannic Rath George H. Booth Simple Fermionic backflow states via a systematically improvable tensor decomposition Communications Physics |
| title | Simple Fermionic backflow states via a systematically improvable tensor decomposition |
| title_full | Simple Fermionic backflow states via a systematically improvable tensor decomposition |
| title_fullStr | Simple Fermionic backflow states via a systematically improvable tensor decomposition |
| title_full_unstemmed | Simple Fermionic backflow states via a systematically improvable tensor decomposition |
| title_short | Simple Fermionic backflow states via a systematically improvable tensor decomposition |
| title_sort | simple fermionic backflow states via a systematically improvable tensor decomposition |
| url | https://doi.org/10.1038/s42005-025-02083-4 |
| work_keys_str_mv | AT massimobortone simplefermionicbackflowstatesviaasystematicallyimprovabletensordecomposition AT yannicrath simplefermionicbackflowstatesviaasystematicallyimprovabletensordecomposition AT georgehbooth simplefermionicbackflowstatesviaasystematicallyimprovabletensordecomposition |