Anomalous Hall crystal in λ-jellium - a variational Monte Carlo study

Electron crystallization has long been regarded as a hallmark of strongly correlated phases. In recently developed experimental platforms such as two-dimensional van der Waals materials, the interplay between strong interactions and nontrivial quantum geometry has inspired theoretical proposals of crystals with nonzero Chern number, termed anomalous Hall crystals (AHC) [1]. Such AHCs have found in mean-field studies of a topological generalization of the jellium model, called λ-jellium [2]. However, strong correlations are well-known to have a drastic effect on the phase boundaries of electron crystals, calling for methods beyond mean-field theory. Here we address this challenge using state-of-the-art variational Monte Carlo (VMC) with neural-network wavefunctions, accurately capturing quantum fluctuations. We find an anomalous Hall crystal phase remains stable beyond mean-field theory in the presence of finite Berry curvature. Remarkably, quantum geometry in addition dramatically enhances crystallization tendencies, reducing the critical interaction strength to smaller r_s at finite λ.

References:

[1] Dong, Junkai, et al. "Anomalous Hall crystals in rhombohedral multilayer graphene. I. Interaction-driven Chern bands and fractional quantum Hall states at zero magnetic field." Physical Review Letters 133.20 (2024): 206503.

[2] Soejima, Tomohiro, et al. "A Jellium Model for the Anomalous Hall Crystal." arXiv preprint arXiv:2503.12704 (2025).