First-Principles AI finds crystallization of fractional quantum Hall liquids

TL;DR

This paper introduces MagNet, a neural-network variational wavefunction that unifies the description of fractional quantum Hall liquids and electron crystals, enabling discovery of ground states purely through energy minimization.

Contribution

MagNet is a novel AI framework that simultaneously captures fractional quantum Hall states and electron crystals without prior physics knowledge.

Findings

MagNet successfully finds topological liquids and electron crystal ground states.

It operates effectively across various Landau-level mixing regimes.

The approach demonstrates the potential of first-principles AI in strongly correlated quantum systems.

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.