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  • Open Access

First-Principles AI Finds Crystallization of Fractional Quantum Hall Liquids

Ahmed Abouelkomsan* and Liang Fu†

  • *Contact author: ahmed95@mit.edu
  • †Contact author: liangfu@mit.edu
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PRX Intelligence 1, 013010 – Published 11 August, 2026

DOI: https://doi.org/10.1103/9qlr-jp6x

Abstract

When does a fractional quantum Hall (FQH) liquid crystallize? Addressing this question requires a framework that treats fractionalization and crystallization on equal footing, especially in strong Landau-level mixing regime. Here, we introduce MagNet, a self-attention neural-network variational wavefunction designed for quantum systems in magnetic fields on the torus geometry. We show that MagNet provides a unifying and expressive ansatz capable of describing both FQH states and electron crystals within the same architecture. Trained solely by energy minimization of the microscopic Hamiltonian, MagNet discovers topological liquid and electron crystal ground states across a broad range of Landau-level mixing. Our results highlight the power of first-principles artificial intelligence (AI) for solving strongly interacting many-body problems and finding competing phases without external training data or physics preknowledge.

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PRX Intelligence 1, 013010– Published 11 August, 2026
  • Received 1 March 2026
  • Accepted 15 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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