Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2406.17645

Simulating moiré quantum matter with neural network

Di Luo, David D. Dai, Liang Fu

Published Jun 25, 2024• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2406.17645

Related papers

Solving fractional electron states in twisted MoTe$_2$ with deep neural network

Di Luo, Timothy Zaklama, Liang Fu

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 $ν= 1/3$ and various fractional quantum liquids in a unified manner.

arXiv:2503.13585•Mar 17, 2025•1 citation

Emergent Wigner phases in moiré superlattice from deep learning

Xiang Li, Yubing Qian, Weiluo Ren +2 more

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.

arXiv:2406.11134•Communications Physics•Sep 2, 2025•6 citations

Neural Network Discovery of Paired Wigner Crystals in Artificial Graphene

Conor Smith, Yubo Yang, Zhou-Quan Wan +3 more

Moiré systems have emerged as an exciting tunable platform for engineering and probing quantum matter. A large number of exotic states have been observed, stimulating intense efforts in experiment, theory, and simulation. Utilizing a neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moire potential at a filling factor of $ν_m =1/4$ (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form a singlet-like valence bond state which restores local $C_6$ symmetry in hexagonal molecules each spanning $6$ moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré minima mostly depleted. The formation of such a paired Wigner crystal, absent any confining potential or attractive interaction to facilitate "pre-assembling" the molecule, provides a fascinating case of collective phenomena in strongly interacting quantum many-body systems, and opportunities to engineer exotic properties.

quant-pharXiv:2602.16798•Feb 20, 2026•0 citations

Neural Network Discovers Paired Wigner Crystal in Artificial Graphene

Conor Smith, Yubo Yang, Zhou‐Quan Wan +3 more

Abstract Moiré systems have emerged as an exciting new tunable platform for engineering and probing quantum matter. A large number of exotic states have been observed, stimulating intense efforts in experiment, theory, and simulation. Utilizing a neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moiré potential at a filling factor of ν m = 1/4 (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form singlet-like valence bond states which restore local C 6 symmetry in hexagonal molecules each spanning 6 moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré minima mostly depleted. The formation of such a paired Wigner crystal, absent any confining potential or attractive interaction to facilitate "pre-assembling" the molecule, provides a fascinating case of collective phenomena in strongly interacting quantum many-body systems and opportunities to engineer exotic properties in a system within current experimental setups. This discovery signals a new level of predictive power in quantum many-body computations enabled by neural networks and machine learning.

•Apr 29, 2026•0 citations

Ab-Initio Phase Discovery with Neural Quantum States

Smith, Conor

In this thesis we study the quantum many-body problem with tools from machine learning. In particular, we utilize Neural Quantum States (NQS) as an ansatz in Variational Monte Carlo (VMC) simulations. First, we develop a method to train NQS more reliably in an effort to reduce the total computational cost of finding the ground state of strongly-correlated systems. Then, we develop an expressive NQS ansatz to study two-dimensional materials and perform ab-initio phase discovery. In particular, we consider the two-dimensional electron gas, and provide state-of-the-art energies and characterization of the phase diagram. We also find evidence of a novel state between the Fermi liquid and Wigner crystal which we call a Nematic Spin Correlated Liquid (NSCL). Lastly, we turn our attention to a moir\'e system with a honeycomb potential. With minor modifications to the ansatz, we find a highly correlated state we call an interaction-driven molecular Wigner crystal. With the increasing interest in NQS as an accurate method to study the many-body problem and recent advances in experimentally studying two-dimensional materials, we expect the technical developments and physical results presented in this thesis to be valuable to theorists and experimentalists.

•May 17, 2025•0 citations

Pairing-based graph neural network for simulating quantum materials

Di Luo, David D. Dai, Liang Fu

We develop a pairing-based graph neural network for simulating quantum many-body systems. Our architecture augments a BCS-type geminal wavefunction with a generalized pair amplitude parameterized by a graph neural network. Variational Monte Carlo with our neural network simultaneously provides an accurate, flexible, and scalable method for simulating many-electron systems. We apply this method to two-dimensional semiconductor electron-hole bilayers and obtain accurate results on a variety of interaction-induced phases, including the exciton Bose-Einstein condensate, electron-hole superconductor, and bilayer Wigner crystal. Our study demonstrates the potential of physically-motivated neural network wavefunctions for quantum materials simulations.

arXiv:2311.02143•Physical review. B./Physical review. B•Feb 9, 2026•2 citations
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.
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.
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 systems have emerged as an exciting tunable platform for engineering and probing quantum matter. A large number of exotic states have been observed, stimulating intense efforts in experiment, theory, and simulation. Utilizing a neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moire potential at a filling factor of νm=1/4ν_m =1/4νm​=1/4 (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form a singlet-like valence bond state which restores local C6C_6C6​ symmetry in hexagonal molecules each spanning 666 moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré minima mostly depleted. The formation of such a paired Wigner crystal, absent any confining potential or attractive interaction to facilitate "pre-assembling" the molecule, provides a fascinating case of collective phenomena in strongly interacting quantum many-body systems, and opportunities to engineer exotic properties.
Abstract Moiré systems have emerged as an exciting new tunable platform for engineering and probing quantum matter. A large number of exotic states have been observed, stimulating intense efforts in experiment, theory, and simulation. Utilizing a neural-network-based quantum Monte Carlo approach, we discover a new ground state of the two-dimensional electron gas in a honeycomb moiré potential at a filling factor of ν m = 1/4 (one electron every four moiré minima). In this state, two opposite-spin electrons pair to form singlet-like valence bond states which restore local C 6 symmetry in hexagonal molecules each spanning 6 moiré minima. These molecules of pairs then form a molecular Wigner crystal, leaving one quarter of the moiré minima mostly depleted. The formation of such a paired Wigner crystal, absent any confining potential or attractive interaction to facilitate "pre-assembling" the molecule, provides a fascinating case of collective phenomena in strongly interacting quantum many-body systems and opportunities to engineer exotic properties in a system within current experimental setups. This discovery signals a new level of predictive power in quantum many-body computations enabled by neural networks and machine learning.
In this thesis we study the quantum many-body problem with tools from machine learning. In particular, we utilize Neural Quantum States (NQS) as an ansatz in Variational Monte Carlo (VMC) simulations. First, we develop a method to train NQS more reliably in an effort to reduce the total computational cost of finding the ground state of strongly-correlated systems. Then, we develop an expressive NQS ansatz to study two-dimensional materials and perform ab-initio phase discovery. In particular, we consider the two-dimensional electron gas, and provide state-of-the-art energies and characterization of the phase diagram. We also find evidence of a novel state between the Fermi liquid and Wigner crystal which we call a Nematic Spin Correlated Liquid (NSCL). Lastly, we turn our attention to a moir\'e system with a honeycomb potential. With minor modifications to the ansatz, we find a highly correlated state we call an interaction-driven molecular Wigner crystal. With the increasing interest in NQS as an accurate method to study the many-body problem and recent advances in experimentally studying two-dimensional materials, we expect the technical developments and physical results presented in this thesis to be valuable to theorists and experimentalists.
We develop a pairing-based graph neural network for simulating quantum many-body systems. Our architecture augments a BCS-type geminal wavefunction with a generalized pair amplitude parameterized by a graph neural network. Variational Monte Carlo with our neural network simultaneously provides an accurate, flexible, and scalable method for simulating many-electron systems. We apply this method to two-dimensional semiconductor electron-hole bilayers and obtain accurate results on a variety of interaction-induced phases, including the exciton Bose-Einstein condensate, electron-hole superconductor, and bilayer Wigner crystal. Our study demonstrates the potential of physically-motivated neural network wavefunctions for quantum materials simulations.