We study the many-body physics in twisted bilayer graphene coupled to periodic driving of a circularly polarized light. In the limit of high driving frequency $\Omega$, we use Floquet theory to formulate the system by an effective static Hamiltonian truncated to the order of $\Omega^{-2}$, which consists of a single-electron part and the screened Coulomb interaction. We numerically simulate this effective Hamiltonian by extensive exact diagonalization. Remarkably, under appropriate twist angle and driving strength, we identify Floquet fractional Chern insulator states in the partially filled Floquet valence band. We characterize these topologically ordered states by ground-state degeneracy, spectral flow, and entanglement spectrum. We also find topologically trivial charge density waves and interaction-induced Fermi liquid which strongly compete with fractional Chern insulator states.

中文翻译：

---

扭曲双层石墨烯中的 Floquet 分数陈绝缘体和竞争相

我们研究了与周期性驱动圆偏振光耦合的扭曲双层石墨烯中的多体物理。在高驱动频率 $\Omega$ 的限制下，我们使用 Floquet 理论通过截断到 $\Omega^{-2}$ 量级的有效静态哈密顿量来制定系统，该系统由单电子部分和筛选库仑相互作用。我们通过广泛的精确对角化来数值模拟这种有效的哈密顿量。值得注意的是，在适当的扭转角和驱动强度下，我们确定了部分填充的 Floquet 价带中的 Floquet 分数 Chern 绝缘体状态。我们通过基态退化、谱流和纠缠谱来表征这些拓扑有序态。