论文标题
通过高阶拓扑充电动态表征拓扑阶段
Dynamically characterizing topological phases by high-order topological charges
论文作者
论文摘要
我们提出了一种新理论，通过引入高阶拓扑电荷的概念来表征具有非平衡量子动力学的平衡拓扑阶段，并预测了新现象。 Through a dimension reduction approach, we can characterize a $d$-dimensional ($d$D) integer-invariant topological phase with lower-dimensional topological number quantified by high-order topological charges, of which the $s$th-order topological charges denote the monopoles confined on the $(s-1)$th-order band inversion surfaces (BISs) that are $(d-s+1)$D momentum subspaces.批量拓扑由$ s $ th-tord Biss所包含的$ S $ TH订单拓扑指控确定。通过将系统从琐碎阶段到拓扑结构淬灭，我们表明，可以通过高阶动力学散装对应关系检测到后淬火后汉密尔顿的宽敞拓扑，其中高阶拓扑费和高阶Biss均从淬灭动力学中鉴定出来。这种特征理论在两个方面具有重要的优势。首先，最高（$ d $ th）的订单拓扑费用仅为零尺寸（即$ 0 $ th Chern号）的自旋偏振迹象的特征，其尺寸比$ 1 $ ST级阶式拓扑电荷要容易得多，而$ 1 $ ST阶式拓扑费的特征是以较高的尺寸在较高的尺寸空间中连续与电荷相关的自旋纹理。其次，更引人注目的结果是，一阶高整数值拓扑电荷始终减少到具有单位电荷值的多个最高级拓扑电荷，并且在实验中可以很容易地检测到后者。这两个基本特征大大简化了拓扑电荷和拓扑阶段的表征和检测，这将在不久的将来推进实验研究。
We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction approach, we can characterize a $d$-dimensional ($d$D) integer-invariant topological phase with lower-dimensional topological number quantified by high-order topological charges, of which the $s$th-order topological charges denote the monopoles confined on the $(s-1)$th-order band inversion surfaces (BISs) that are $(d-s+1)$D momentum subspaces. The bulk topology is determined by the $s$th order topological charges enclosed by the $s$th-order BISs. By quenching the system from trivial phase to topological regime, we show that the bulk topology of post-quench Hamiltonian can be detected through a high-order dynamical bulk-surface correspondence, in which both the high-order topological charges and high-order BISs are identified from quench dynamics. This characterization theory has essential advantages in two aspects. First, the highest ($d$th) order topological charges are characterized by only discrete signs of spin-polarization in zero dimension (i.e. the $0$th Chern numbers), whose measurement is much easier than the $1$st-order topological charges that are characterized by the continuous charge-related spin texture in higher dimensional space. Secondly, a more striking result is that a first-order high integer-valued topological charge always reduces to multiple highest-order topological charges with unit charge value, and the latter can be readily detected in experiment. The two fundamental features greatly simplify the characterization and detection of the topological charges and also topological phases, which shall advance the experimental studies in the near future.
