Quantum Geometry Driven Crystallization: A Neural-Network Variational Monte Carlo Study

TL;DR

This study uses neural-network variational Monte Carlo to explore how quantum geometry influences Wigner crystallization, revealing that quantum effects significantly stabilize and enhance crystal formation beyond mean-field predictions.

Contribution

It demonstrates that quantum geometry and fluctuations stabilize and promote crystallization in a tunable model, extending understanding beyond mean-field results.

Findings

Quantum fluctuations do not destroy the anomalous Hall crystal.

Quantum geometric effects dramatically enhance crystallization.

Crystals are stabilized at densities much higher than mean-field predictions.

Abstract

Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with relatively flat bands and pronounced Berry curvature has added fresh urgency to this question. Recent mean-field studies have proposed a topological variant of the Wigner crystal, the anomalous Hall crystal (AHC), with non-zero Chern number. However it remains unclear whether the AHC survives beyond the mean-field approximation. Here, we map out the ground-state phase diagram of the $\lambda$-jellium model - a simple model whose interaction strength and Berry curvature are independently tunable - using state-of-the-art neural-network variational Monte Carlo. The AHC is found to remain stable against quantum fluctuations. Surprisingly, quantum geometric effects are found to dramatically enhance crystallization. Both the AHC and the standard Wigner Crystal are stabilized at densities up to an order of magnitude above the critical density in the absence of quantum geometry, yet still significantly below the threshold predicted by mean-field theory. These striking results highlight the rich interplay between quantum fluctuations, quantum geometry, and crystallization, providing concrete guidance for experiments and enabling future explorations of fractionalized crystals and chiral superconductors.