Emergent Wigner phases in moiré superlattice from deep learning

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 identifies diverse quantum states, including emergent phases such as generalized Wigner crystals, Wigner molecular crystals, and Wigner covalent crystals. These discoveries provide insights into recent experimental studies and suggest more 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. In this work the authors employ neural network wavefunctions to discover correlated electron phases in moiré superlattices. Their approach identifies multiple emergent Wigner phases, including generalized crystals, molecular crystals, and a covalent crystal state.