论文标题
部分可观测时空混沌系统的无模型预测
Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
论文作者
论文摘要
除了众所周知的单粒子系统拓扑结构理论之外，表征相互作用的多粒子量子系统的拓扑性质是一个巨大的挑战。在这里，我们发现了通过扭曲边界条件（TBC）定义的拓扑不变性与多粒子系统中的质量（C.M.）动量状态之间的关系。我们发现，通过TBC定义的浆果相可以从C.M.配方的多粒子Wilson环上获得。势头状态。由于Chern数字可以写成浆果阶段的绕组，因此我们证明了通过TBC和C.M.获得的Chern数量的等效性。动量状态接近。作为原则示例，我们研究了Aubry-andr {é} -harper（aah）模型的拓扑特性。我们的数值结果表明TBC接近和C.M.对于多体案例和几个身体案例，方法彼此彼此一致。我们的工作奠定了混凝土基础，并为探索多粒子拓扑状态提供了新的见解。
Beyond the well-known topological band theory for single-particle systems, it is a great challenge to characterize the topological nature of interacting multi-particle quantum systems. Here, we uncover the relation between topological invariants defined through the twist boundary condition (TBC) and the center-of-mass (c.m.) momentum state in multi-particle systems. We find that the Berry phase defined through TBC can be equivalently obtained from the multi-particle Wilson loop formulated by c.m. momentum states. As the Chern number can be written as the winding of the Berry phase, we consequently prove the equivalence of Chern numbers obtained via TBC and c.m. momentum state approaches. As a proof-of-principle example, we study topological properties of the Aubry-Andr{é}-Harper (AAH) model. Our numerical results show that the TBC approach and c.m. approach are well consistent with each other for both many-body case and few-body case. Our work lays a concrete foundation and provides new insights for exploring multi-particle topological states.
