AI 中文总结
该研究推导半无限链的体边对应关系，通过解析延拓布洛赫哈密顿量至复波矢，利用其零点、例外点推导绕数以计数受手征对称性保护的拓扑边界态。
AI 中文摘要
我们对半无限链的体边对应关系提供了另一种推导方法。为描述边界态，我们将常规布洛赫哈密顿量解析延拓至复波矢k。首先，我们注意到布洛赫波函数的零点与边界态相关，至少在仅存在最近邻跃迁的系统中成立。我们证明，具有手征对称性的解析延拓布洛赫哈密顿量存在例外点，此处两个不同态发生合并；这些特殊点与边界态的绝热保护相关。我们推导了一个绕数，用于计数受手征对称性保护的拓扑边界态数量。
英文摘要
We provide an alternative derivation of the bulk-boundary correspondence for semi-infinite chains. To describe edge states, we analytically continue the usual Bloch Hamiltonian to complex wave vectors $k$. To start, we note that the zeros of a Bloch wavefunction are related to edge states, at least in systems with nearest-neighbour hoppings. We show that an analytically continued Bloch Hamiltonian with chiral symmetry has exceptional points, where two different states coalesce. These special points are related to the adiabatic protection of edge states. We derive a winding number that counts the number of topological edge states protected by chiral symmetry.
Comments11 pages, 4 figures
