Motivated by recent experimental work on moiré systems in a strong magnetic field, we compute the compressibility as well as the spin correlations and Hofstadter spectrum of spinful electrons on a honeycomb lattice with Hubbard interactions using the determinantal quantum Monte Carlo method. While the interactions in general preserve quantum and anomalous Hall states, emergent features arise corresponding to an antiferromagnetic insulator at half-filling and other incompressible states following the Chern sequence ± (2N + 1). These odd integer Chern states exhibit strong ferromagnetic correlations and arise spontaneously without any external mechanism for breaking the spin-rotation symmetry. Analogs of these magnetic states should be observable in general interacting quantum Hall systems. In addition, the interacting Hofstadter spectrum is qualitatively similar to the experimental data at intermediate values of the on-site interaction.

受近期强磁场中莫尔系统实验工作的启发，我们使用行列式量子蒙特卡洛方法计算了蜂窝晶格上具有哈伯德相互作用的可压缩性以及自旋相关性和自旋电子的 Hofstadter 谱。虽然相互作用通常会保留量子和反常霍尔态，但出现的特征对应于处于半填充状态的反铁磁绝缘体和其他不可压缩状态，遵循 Chern 序列 ± (2 N + 1). 这些奇整数陈态表现出很强的铁磁相关性，并且在没有任何外部机制破坏自旋旋转对称性的情况下自发产生。在一般相互作用的量子霍尔系统中应该可以观察到这些磁态的类似物。此外，相互作用的 Hofstadter 光谱与现场相互作用中间值的实验数据在性质上相似。