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arXiv:2406.11134 · Communications Physics

Emergent Wigner phases in moiré superlattice from deep learning

Xiang Li, Yubing Qian, Weiluo Ren, Yang Xu, Ji Chen

Published Sep 2, 2025• 6 citations
arXivHTMLPDF

Abstract

Abstract Moiré superlattice designed in stacked van der Waals material provides a dynamic platform for hosting exotic and emergent condensed matter phenomena. However, the relevance of strong correlation effects and the large size of moiré unit cells pose significant challenges for traditional computational techniques. To overcome these challenges, we develop an unsupervised deep learning approach to uncover electronic phases emerging from moiré systems based on variational optimization of neural network many-body wavefunction. Our approach has identified diverse quantum states, including novel phases such as generalized Wigner crystals, Wigner molecular crystals, and previously unreported Wigner covalent crystals. These discoveries provide insights into recent experimental studies and suggest new phases for future exploration. They also highlight the crucial role of spin polarization in determining Wigner phases. More importantly, our proposed deep learning approach is proven general and efficient, offering a powerful framework for studying moiré physics.

DOI
10.1038/s42005-025-02282-z

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Abstract Moiré superlattice designed in stacked van der Waals material provides a dynamic platform for hosting exotic and emergent condensed matter phenomena. However, the relevance of strong correlation effects and the large size of moiré unit cells pose significant challenges for traditional computational techniques. To overcome these challenges, we develop an unsupervised deep learning approach to uncover electronic phases emerging from moiré systems based on variational optimization of neural network many-body wavefunction. Our approach has identified diverse quantum states, including novel phases such as generalized Wigner crystals, Wigner molecular crystals, and previously unreported Wigner covalent crystals. These discoveries provide insights into recent experimental studies and suggest new phases for future exploration. They also highlight the crucial role of spin polarization in determining Wigner phases. More importantly, our proposed deep learning approach is proven general and efficient, offering a powerful framework for studying moiré physics.
Moiré materials provide an ideal platform for exploring quantum phases of matter. However, solving the many-electron problem in moiré systems is challenging due to strong correlation effects. We introduce a powerful variational representation of quantum states, many-body neural Bloch wavefunction, to solve many-electron problems in moiré materials accurately and efficiently. Applying our method to the semiconductor heterobilayer WSe2/WS2 , we obtain a generalized Wigner crystal at filling factor n = 1/3, a Mott insulator n = 1, and a correlated insulator with local magnetic moments and antiferromagnetic spin correlation at n = 2. Our neural network approach improves the simulation accuracy of strongly interacting moiré materials and paves the way for discovery of new quantum phases with variational learning principle in a unified framework.
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Solving fractional electron states in twisted MoTe2_22​ with deep neural network
The emergence of moiré materials, such as twisted transition-metal dichalcogenides (TMDs), has created a fertile ground for discovering novel quantum phases of matter. However, solving many-electron problems in moiré systems presents significant challenges due to strong electron correlation and strong moiré band mixing. Recent advancements in neural quantum states hold the promise for accurate and unbiased variational solutions. Here, we introduce a powerful neural wavefunction to solve ground states of twisted MoTe2 across various fractional fillings, reaching unprecedented accuracy and system size. From the full structure factor and quantum weight, we conclude that our neural wavefunction accurately captures both the electron crystal at ν=1/3ν= 1/3ν=1/3 and various fractional quantum liquids in a unified manner.
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