Résumé
In this talk, I will present an overview of the study of the modulated electron gas in 2 dimensions using Neural Quantum States. The work is based on the Multi-Planewave Message-Passing Neural Quantum State (MP2NQS), an accurate wavefunction ansatz designed for real-space quantum Monte Carlo simulations. MP2NQS integrates a traditional Slater-Jastrow-Backflow wavefunction with a powerful message-passing graph neural network architecture for both Jastrow and Backflow functions, alongside aggressive orbital optimization in a plane-wave basis. This powerful approach achieves ground-state accuracy for the electron gas that rivals, and often surpasses, state-of-the-art diffusion quantum Monte Carlo (DMC) calculations. By performing orbital optimization in the presence of an accurate description of electron correlation, the approach can successfully locate phase transitions with little human input.
Using this ansatz, we have re-investigated the homogeneous 2D electron gas, achieving consistent improvements over prior DMC results. Notably, we identify the fluid-to-Wigner crystal phase transition at a critical density defined by rs∼37±1, lower than previously reported. More importantly, our results uncover pronounced short-range nematic spin correlations across a wide density range in the fluid phase. I will also discuss recent applications to Moiré continuum Hamiltonians modeling transition metal dichalcogenide (TMD) bilayers. These studies examine the effects of Moiré potential depth, gate screening, and hole doping on ground-state properties, offering new insights into correlated phases in these systems. Finally, I will present a study of the influence of impurities on the properties of the electron gas, illustrating a strong interplay between disorder and electron localization.
