In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.

中文翻译：

---

无序 Floquet 系统的流动方程

在这项工作中，我们提出了一种基于流动方程的无序、周期性驱动（Floquet）量子多体系统的新方法。具体来说，我们在扩展的 Hilbert 空间中引入了 Floquet 算子的连续酉流，其不动点既是对角线又是时间无关的，允许我们直接获得 Floquet 模式。我们首先将这种方法应用于周期性驱动的安德森绝缘体，它是精确的，然后将其扩展到截断流动方程 ansatz 内的驱动多体局部系统。特别地，我们计算了运动的紧急 Floquet 局部积分，该积分表征了周期性驱动的多体局部化相位。我们证明该方法在弱相互作用机制中保持良好控制，并允许我们访问比精确数值方法访问更大的系统大小，