Neural Network Fractional Quantum Hall States with Learnable Orbital Pair Matrix Factors: Balancing Physical Priors and Flexibility
Abstract
Neural network fractional quantum Hall (FQH) states offer a promising alternative for capturing Landau level (LL) mixing and for understanding FQH physics, yet the incorporation of physical priors has so far been limited to the minimal exact constraints built into the ansatz. Working in spherical geometry, we show that the network's flexibility suffers both when only minimal additional physical priors are supplied and when priors such as flux attachment are imposed rigidly. In the former case, the monopole harmonic product orbital (MHPO) ansatz is difficult to optimize, whereas in the latter, the expressivity of the neural network is restricted. We therefore propose the orbital pair matrix factor MHPO (MHPO-M) ansatz, which balances physical priors against flexibility by not only replacing the fixed Laughlin structure with learnable pair factors but also making them dependent on both the electron configurations and the orbitals. Across ν=1/5, 1/3, and 2/5, MHPO-M achieves the lowest variational energy among the tested variants, and a factorized orbital readout based on it enables scaling to 35 electrons, with energies competitive with trends inferred from three-LL exact-diagonalization results. These results demonstrate that physical priors can be appropriately incorporated without sacrificing the flexibility of neural network wavefunctions, opening a promising path toward accurate, scalable modeling of FQH systems with LL mixing.
Related
- PINN-LPCDD: Physics-Informed Neural Network with Learnable and Physically Consistent Domain Decomposition for Compressible Multi-Medium Flows
- Statistically Robust Characterization of Polaron and Bipolaron Intrinsic Traps in Amorphous Silica Reveals the Role of Network Flexibility in Electron Localisation
- Hard-Constrained Physics--Informed Neural Network with Adaptive Regional Residual Balancing for the Generalized Falkner--Skan Problem
- Physical-Prior-Guided Spectral Token Network for Vector Bending Demodulation of Multicore Fiber Bragg Gratings
- FLAT: Smoothing the Rugged Landscape for Learnable, Sample-Efficient Traffic Calibration
BibTeX
@misc{qian2026neural,
title = {{Neural Network Fractional Quantum Hall States with Learnable Orbital Pair Matrix Factors: Balancing Physical Priors and Flexibility}},
author = {Yubing Qian and Weiluo Ren and Ji Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28095},
eprint = {2610.28095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28095},
}
RIS
TY - UNPB
TI - Neural Network Fractional Quantum Hall States with Learnable Orbital Pair Matrix Factors: Balancing Physical Priors and Flexibility
AU - Yubing Qian
AU - Weiluo Ren
AU - Ji Chen
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28095
UR - https://arxiv.org/abs/2610.28095
AB - Neural network fractional quantum Hall (FQH) states offer a promising alternative for capturing Landau level (LL) mixing and for understanding FQH physics, yet the incorporation of physical priors has so far been limited to the minimal exact constraints built into the ansatz. Working in spherical geometry, we show that the network's flexibility suffers both when only minimal additional physical priors are supplied and when priors such as flux attachment are imposed rigidly. In the former case, the monopole harmonic product orbital (MHPO) ansatz is difficult to optimize, whereas in the latter, the expressivity of the neural network is restricted. We therefore propose the orbital pair matrix factor MHPO (MHPO-M) ansatz, which balances physical priors against flexibility by not only replacing the fixed Laughlin structure with learnable pair factors but also making them dependent on both the electron configurations and the orbitals. Across ν=1/5, 1/3, and 2/5, MHPO-M achieves the lowest variational energy among the tested variants, and a factorized orbital readout based on it enables scaling to 35 electrons, with energies competitive with trends inferred from three-LL exact-diagonalization results. These results demonstrate that physical priors can be appropriately incorporated without sacrificing the flexibility of neural network wavefunctions, opening a promising path toward accurate, scalable modeling of FQH systems with LL mixing.
ER -