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Peer-reviewedCC BY-NC-NDProceedings of the National Academy of Sciences

Neural network–augmented Pfaffian wave-functions for scalable simulations of interacting fermions

  • Ao Chen1,2,3
  • Zhou‐Quan Wan1
  • Anirvan M. Sengupta4,1,5
  • Antoine Georges1,6,7,8
  • Christopher Roth1
8 affiliations
  1. 1Center for Computational Quantum Physics, Flatiron Institute
  2. 2Division of Chemistry and Chemical Engineering, California Institute of Technology
  3. 3Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg
  4. 4Center for Computational Mathematics, Flatiron Institute
  5. 5Department of Physics and Astronomy, Rutgers University
  6. 6Centre de Physique Théorique, CNRS, École Polytechnique, IP Paris
  7. 7Collège de France
  8. 8Department of Quantum Matter Physics, Université de Genève
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Abstract

Developing accurate numerical methods for strongly interacting fermions is crucial for improving our understanding of various quantum many-body phenomena, especially unconventional superconductivity. Recently, neural quantum states have emerged as a promising approach for studying correlated fermions, highlighted by the hidden fermion and backflow methods, which use neural networks to model corrections to fermionic quasiparticle orbitals. In this work, we expand these ideas to the space of Pfaffians, a wave-function that naturally expresses superconducting pairings, and propose the hidden fermion Pfaffian state (HFPS), which flexibly represents both unpaired and superconducting phases and scales to large systems with favorable asymptotic complexity. In our numerical experiments, HFPS provides state-of-the-art variational accuracy in different regimes of both the attractive and repulsive Hubbard models. We show that the HFPS is able to capture general phases with and without pairing, and therefore may be a useful tool for modeling phases with unconventional superconductivity.

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Cite

BibTeXRIS
BibTeX
@article{chen2026neural,
  title = {{Neural network–augmented Pfaffian wave-functions for scalable simulations of interacting fermions}},
  author = {Ao Chen and Zhou‐Quan Wan and Anirvan M. Sengupta and Antoine Georges and Christopher Roth},
  journal = {Proceedings of the National Academy of Sciences},
  year = {2026},
  month = aug,
  doi = {10.1073/pnas.2535288123},
  url = {https://doi.org/10.1073/pnas.2535288123},
  note = {CC BY-NC-ND},
}
RIS
TY  - JOUR
TI  - Neural network–augmented Pfaffian wave-functions for scalable simulations of interacting fermions
AU  - Ao Chen
AU  - Zhou‐Quan Wan
AU  - Anirvan M. Sengupta
AU  - Antoine Georges
AU  - Christopher Roth
PY  - 2026
DA  - 2026/08/28
JO  - Proceedings of the National Academy of Sciences
DO  - 10.1073/pnas.2535288123
UR  - https://doi.org/10.1073/pnas.2535288123
AB  - Developing accurate numerical methods for strongly interacting fermions is crucial for improving our understanding of various quantum many-body phenomena, especially unconventional superconductivity. Recently, neural quantum states have emerged as a promising approach for studying correlated fermions, highlighted by the hidden fermion and backflow methods, which use neural networks to model corrections to fermionic quasiparticle orbitals. In this work, we expand these ideas to the space of Pfaffians, a wave-function that naturally expresses superconducting pairings, and propose the hidden fermion Pfaffian state (HFPS), which flexibly represents both unpaired and superconducting phases and scales to large systems with favorable asymptotic complexity. In our numerical experiments, HFPS provides state-of-the-art variational accuracy in different regimes of both the attractive and repulsive Hubbard models. We show that the HFPS is able to capture general phases with and without pairing, and therefore may be a useful tool for modeling phases with unconventional superconductivity.
SN  - 0027-8424
SN  - 1091-6490
ER  -