二维手征对称系统中拓扑无隙相位的Loschirton回波显示
Manifestation of a topological gapless phase in a two-dimensional chiral symmetric system through Loschmidt echo
摘要：
与拓扑绝缘体的边缘态的能级位于体能隙中不同，拓扑半金属的边缘态隐藏在体光谱中，很难通过能量来识别。通过一个具体的二维手征对称晶格模型，研究了拓扑半金属无带隙相的体态和边态对无序微扰的敏感性。拓扑无隙相的特征在于动量空间中的两个相反的涡旋和非零的缠绕数，这对应于当施加开边界条件时的边缘平带。对于这个系统，数值计算结果表明，一个显着的特点是，对弱无序的边缘状态的鲁棒性和平带边缘模式保持锁定在零能量的存在下，弱手征对称性保留的障碍。我们采用体态和边态的Loschlessecho（LE）来研究无序微扰的动力学效应。我们发现，对于一个初始的体状态，LE指数衰减，而它收敛到一个常数的初始边缘状态在弱无序的存在。此外，收敛LE可以用来识别涡的位置以及相图。我们讨论了实现这样的动态调查的拓扑光子系统。
英文摘要：
Unlike the edge state of a topological insulator where its energy level lives in the bulk energy gap, the edge state of a topological semimetal hides in the bulk spectrum and is difficult to be identified by the energy. We investigate the sensitivity of bulk and edge states of the gapless phase for a topological semimetal to the disordered perturbation via a concrete two-dimensional chiral symmetric lattice model. The topological gapless phase is characterized by two opposite vortices in the momentum space and nonzero winding numbers, which correspond to the edge flatband when the open boundary condition is applied. For this system, numerical results reveal that a distinguishing feature is that the robustness of the edge states against weak disorder and the flatband edge modes remain locked at zero energy in the presence of weak chiral-symmetry-preserving disorder. We employ the Loschmidt echo (LE) for both bulk and edge states to study the dynamic effect of disordered perturbation. We show that, for an initial bulk state, the LE decays exponentially, whereas it converges to a constant for an initial edge state in the presence of weak disorder. Furthermore, the convergent LE can be utilized to identify the positions of vortices as well as the phase diagram. We discuss the realization of such dynamic investigations in a topological photonic system.
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