论文标题
许多身体Chern绝缘子的单一制备：绝热的边界对应关系
Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
论文作者
论文摘要
我们解决了准备不平衡的多体切绝缘子（CI）和相关的散装式对应关系的长期问题。本文中，通过构建动态多体的Chern不变性来解决这一问题，该动力学利用了CI的块状宏观电动极化（Resta极化）的特性。还建立了由可观察到的相关性定义的Chern不变性，以拓泊地对许多平衡中的许多身体态分类。通过将石墨烯的范式haldane模型从拓扑阶段升至拓扑阶段，可以探测不变的不平衡行为。我们表明，非线性坡道可能在接近拓扑状态方面更有效地发挥作用，从而确立了最佳的拓扑状态制备的存在。此外，为了确保跨量子临界点的几乎绝热动态，我们提出了一种新型的反浸润方案。通过观察出现的$ U（1）$拓扑费来确定准备状态的拓扑性质。我们还计算在半周期边界条件下系统进化状态的边缘电流，并清楚地建立了绝热的散装式对应关系，该对应牢固地巩固了多体不变的有效性。
We approach the long-standing problem of preparing an out-of-equilibrium many-body Chern insulator (CI) and associated bulk-boundary correspondence unitarily. Herein, this is addressed by constructing a dynamical many-body Chern invariant exploiting the property of the bulk macroscopic electric polarisation (Resta polarisation) of the CI. This Chern invariant defined from observable correlations is also established to topologically classify many body Chern states in equilibrium. The non-equilibrium behavior of the invariant is probed by ramping the paradigmatic Haldane model of graphene from its trivial to the topological phase. We show that a non-linear ramp may work more efficiently in approaching the topological state, thereby establishing the existence of an optimal topological state preparation. Furthermore, to ensure the near adiabatic dynamics across the quantum critical point, we propose a novel counter-diabatic scheme. The topological nature of the prepared state is firmly established by observing an emerging $U(1)$ topological charge. We also compute the edge current in the time evolved state of the system under a semi-periodic boundary condition and clearly establish an adiabatic bulk-boundary correspondence which firmly ensconces the validity of the many-body invariant.
