First-Principles AI finds crystallization of fractional quantum Hall liquids

2026-02-03

AI Summary

This work investigates how fractional quantum Hall liquids compete with and ultimately crystallize into electron solids under strong Landau level mixing. To address this, we introduce MagNet—a variational neural wave function based on self-attention mechanisms—trained solely by minimizing the energy of the microscopic Hamiltonian on a torus geometry, without reliance on external data or physical priors. For the first time, this approach enables a unified, first-principles identification of ground states across a broad parameter regime, automatically distinguishing between fractional quantum Hall phases and electron crystalline orders. Our results demonstrate the remarkable capacity of artificial intelligence to uncover competing quantum phases in strongly correlated many-body systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Humans and AI: Human-in-the-loop Machine Learning
• Multiagent Systems: Multiagent Learning

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Web Mining and Content Analysis: Large pretrained models with web data
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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 AI for solving strongly interacting many-body problems and finding competing phases without external training data or physics pre-knowledge.

Problem

• fractional quantum Hall
• crystallization
• Landau-level mixing
• many-body problem
• electron crystal

Innovation

• MagNet
• fractional quantum Hall
• electron crystal
• first-principles AI
• variational wavefunction