论文标题
指数增长的散装绿色功能是一个维度的非平凡的非缠绕数的签名
Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension
论文作者
论文摘要
非零的非季节绕组数表明，由于其哈密顿量的非热性性，间隙系统处于非平凡的拓扑类别。尽管对于赫尔米尼系统，而边缘状态的存在反映了非平凡的拓扑量子数，但非零的非铁绕组数量会影响系统的批量响应。为了建立这种关系，我们介绍了批量的绿色函数，该功能描述了在诱导的激发尚未传播到边界的时间尺度上，散布系统对外部扰动的响应，如果非避风动物的绕组数为非零，则表明它将在空间中生长。这种空间增长解释了为什么非热系统在较长时间尺度上的响应（在较长的时间尺度上反复反映在边界上的激发）可能对边界条件高度敏感。对边界条件的这种指数敏感性解释了非热式系统中散装对应关系的分解：针对周期性边界条件计算的拓扑不变性不再预测开放边界条件的边界状态的存在或不存在。
A nonzero non-Hermitian winding number indicates that a gapped system is in a nontrivial topological class due to the non-Hermiticity of its Hamiltonian. While for Hermitian systems nontrivial topological quantum numbers are reflected by the existence of edge states, a nonzero non-Hermitian winding number impacts a system's bulk response. To establish this relation, we introduce the bulk Green function, which describes the response of a gapped system to an external perturbation on timescales where the induced excitations have not propagated to the boundary yet, and show that it will grow in space if the non-Hermitian winding number is nonzero. Such spatial growth explains why the response of non-Hermitian systems on longer timescales, where excitations have been reflected at the boundary repeatedly, may be highly sensitive to boundary conditions. This exponential sensitivity to boundary conditions explains the breakdown of the bulk-boundary correspondence in non-Hermitian systems: topological invariants computed for periodic boundary conditions no longer predict the presence or absence of boundary states for open boundary conditions.
