Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly non-local Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Due to disorder, inhomogeneities appear in the spatial distribution of the local Chern marker. Their size exhibits power-law scaling with the critical exponent matching the one extracted from the Berry curvature of a clean system. We drive the system slowly through such a quantum phase transition. The characteristic size of inhomogeneities in the non-equilibrium post-quench state obeys the Kibble-Zurek scaling. In this setting, the local Chern marker thus does behave in a similar way as a local order parameter for a symmetry breaking second order phase transition. The Kibble-Zurek scaling also holds for the inhomogeneities in the spatial distribution of excitations and of the orbital polarization.

中文翻译：

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无序Chern绝缘子的Kibble-Zurek行为

即使对于Chern绝缘子中的拓扑量子相变，在Landau理论的意义上不存在局部阶跃参数，但高度非局部的Berry曲率在量子临界点附近仍表现出临界行为。我们在弱无序的Chern绝缘子中研究了其真实空间模拟物（本地Chern标记）的关键特性。由于紊乱，局部切恩标记的空间分布中会出现不均匀性。它们的大小表现出幂律定标，并且临界指数与从干净系统的Berry曲率中提取的临界指数匹配。我们通过这种量子相变来缓慢地驱动系统。非平衡淬火后非均匀状态的特征尺寸服从Kibble-Zurek缩放。在这种情况下，因此，本地Chern标记的行为与对称中断二阶相变的本地阶参类似。Kibble-Zurek标度还适用于激发空间分布和轨道极化的不均匀性。