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...

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Main Authors: Massimo Bortone, Yannic Rath, George H. Booth
Format: Article
Language:English
Published: Nature Portfolio 2025-04-01
Series:Communications Physics
Online Access:https://doi.org/10.1038/s42005-025-02083-4
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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.
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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
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