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Solving and visualizing fractional quantum Hall wavefunctions with neural network

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arxiv 2412.00618 v2 pith:JFI6VEKW submitted 2024-11-30 cond-mat.str-el cond-mat.dis-nnquant-ph

Yi Teng , David D. Dai , Liang Fu This is my paper · ORCID
classification cond-mat.str-elcond-mat.dis-nnquant-ph
keywords electronmixingfractionalhallnetworkneuralquantumsolving
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abstract

We introduce an attention-based fermionic neural network (FNN) to variationally solve the problem of two-dimensional Coulomb electron gas in magnetic fields, a canonical platform for fractional quantum Hall (FQH) liquids, Wigner crystals and other unconventional electron states. Working directly with the full Hilbert space of $N$ electrons confined to a disk, our FNN consistently attains energies lower than LL-projected exact diagonalization (ED) and learns the ground state wavefunction to high accuracy. In low LL mixing regime, our FNN reveals microscopic features in the short-distance behavior of FQH wavefunction beyond the Laughlin ansatz. For moderate and strong LL mixing parameters, the FNN outperforms ED significantly. Moreover, a phase transition from FQH liquid to a crystal state is found at strong LL mixing. Our study demonstrates unprecedented power and universality of FNN based variational method for solving strong-coupling many-body problems with topological order and electron fractionalization.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hyperdeterminant wavefunctions

    cond-mat.str-el 2026-07 conditional novelty 7.5 of 10

    Hyperdeterminant wavefunctions with a locality structure, plus VMPI effective theories and projective expansion, give a practical variational framework for fractional Chern insulators and quantum spin liquids.

  2. Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model

    cond-mat.dis-nn 2025-05 conditional novelty 6.0 of 10

    Irrep-resolved GCNN variational energies indicate a 4-fold degenerate columnar ground state for V <= 0.4 in the square-lattice quantum dimer model, shifting possible plaquette or mixed ordering to 0.4 < V < 1.

  3. Is attention all you need to solve the correlated electron problem?

    cond-mat.str-el 2025-02 conditional novelty 6.0 of 10

    A self-attention neural network wavefunction gives lower variational energies than band-projected exact diagonalization for a moiré electron model and shows a roughly quadratic parameter scaling with electron number.

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