发表机构
ETH Zürich; Institute of Theoretical Physics, Chinese Academy of Sciences; University of Chinese Academy of Sciences; École Polytechnique Fédérale de Lausanne (EPFL)（苏黎世联邦理工学院; 中国科学院理论物理研究所; 中国科学院大学; 洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用神经量子态方法，揭示了莫尔材料中强关联可诱导相关金属相及自旋依赖的分子绝缘体转变，产生亚磁性与轨道向列序，且结果对相互作用模型具有鲁棒性。
AI 中文摘要
在本工作中，我们研究了一个二维电子连续介质模型，该模型中的电子通过长程库仑力相互作用，并受到填充因子ν=2时三角周期势的作用。利用基于消息传递神经网络并通过变分蒙特卡洛优化的神经量子态，我们确定了基态相图随周期势强度和塞曼场的变化关系。尽管非相互作用系统预期会形成常规能带绝缘体，但我们表明强关联可以定性地重塑绝缘态，并在部分相图中抑制能带绝缘体，转而支持相关金属相，两相之间由一级相变分隔。此外，金属-绝缘体转变表现出对自旋极化的强烈依赖：非极化系统通过形成s波分子绝缘体而在显著较弱的周期势下变为绝缘体，其中相反自旋的电子在每个势能最小值附近结合；而完全极化系统则需要显著更深的势能，并转而形成对称性破缺的轨道向列分子晶体。这种自旋依赖的分子转变导致了磁化曲线的不连续性、亚磁转变以及相图中的多个多临界点，并在密度分布、实空间关联函数和结构因子中呈现清晰的特征。为进一步阐明库仑相互作用长程特性的作用，我们还研究了可在超冷原子平台上实现的短程排斥相互作用。我们发现多体相图的定性结构保持不变，证明了我们的结果在不同相互作用模型下的鲁棒性。
英文摘要
In this work, we investigate a continuum model of two-dimensional electrons interacting via long-range Coulomb forces and subject to a triangular periodic potential at filling factor $ν=2$. Using neural quantum states based on message-passing neural networks optimized with variational Monte Carlo, we determine the ground-state phase diagram as a function of periodic potential strength and Zeeman field. Although the noninteracting system is expected to form a conventional band insulator, we show that strong correlations can qualitatively reshape the insulating state and, in part of the phase diagram, suppress the band insulator in favor of a correlated metallic phase, with a first-order transition separating the two regimes. Moreover, the metal--insulator transition exhibits a strong dependence on spin polarization: the unpolarized system becomes insulating at substantially weaker periodic potentials through the formation of an $s$-wave molecular insulator, where opposite-spin electrons bind near each potential minimum, whereas the fully polarized system requires a significantly deeper potential and instead forms a symmetry-broken orbital nematic molecular crystal. This spin-dependent molecular transition gives rise to discontinuous magnetization curves, metamagnetic transitions, and several multicritical points in the phase diagram, together with clear signatures in the density profiles, real-space correlation functions, and structure factors. To further elucidate the role of the long-range character of the Coulomb interaction, we also study short-range repulsive interactions, which can be realized with ultracold-atom platforms. We find that the qualitative structure of the many-body phase diagram remains unchanged, demonstrating the robustness of our results across different interaction models.
