In finite systems driven unitarily across topological phase transitions, the Chern number and the Bott index have been found to exhibit different behaviors depending on the boundary conditions and on the commensurability of the lattice. For periodic boundary conditions, the Chern number does not change for finite commensurate lattices (or in the thermodynamic limit). On the other hand, the Chern number can change for incommensurate lattices with periodic boundary conditions and the Bott index can change for lattices with open boundary conditions. Here we show that the scalings of the fields at which those two indices change exhibit Landau-Zener and near-adiabatic regimes depending on the speed at which the strength of the drive is ramped up and on the system size. Those regimes are preceded by a regime in which the topological indices do not change. The latter is the only regime that, for nonvanishing ramp speeds, survives in the thermodynamic limit. We then show that the dc Hall response can be used to detect topological phase transitions independently of the behavior of the topological indices.

中文翻译：

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动态拓扑相变中的通用Landau-Zener体制

在跨拓扑相变整体驱动的有限系统中，已发现切尔数和波特指数根据边界条件和晶格的可比性表现出不同的行为。对于周期性边界条件，有限的相应晶格（或在热力学极限范围内）的Chern数不变。另一方面，对于具有周期性边界条件的不相称晶格，切恩数可以改变，对于具有开放边界条件的晶格，Bott指数可以变化。在这里，我们表明，这两个指数变化的领域的标度表现出Landau-Zener和接近绝热的状态，这取决于驱动器强度提高的速度和系统的大小。在那些方案之前是拓扑索引不变的方案。对于不消失的斜坡速度，后者是唯一能够在热力学极限内生存的状态。然后，我们证明直流霍尔响应可用于独立于拓扑索引行为检测拓扑相变。