论文标题
Trimer Su-Schrieffer-Heeger模型中的散装对应关系
Bulk-edge correspondence in the trimer Su-Schrieffer-Heeger model
论文作者
论文摘要
Trimer Su-Schrieffer-Heeger（SSH3）模型的一个显着特征是它支持局部边缘状态。尽管Zak的相位对于镜像对称链的情况仍然进行了量化，但众所周知，在没有这种对称性的情况下，它无法采用整数值，因此在一般情况下，它无法扮演明确定义的散装不变性的作用。试图通过格林的功能或扩展到合成维度来建立批量的对应关系。在这里，我们提出了一种简单的SSH3替代方案，利用先前引入的Sublattice Zak的相位，在没有镜像对称性和非固定链的情况下，该阶段也仍然有效。定义的大量数量需要整数值，是规格不变的，可以解释为参考和目标哈密顿量之间边缘状态数量的差。我们的推导进一步预测了有限开放链的确切校正，可以简单地概括，并在此模型中调用类似手性的对称性。
A remarkable feature of the trimer Su-Schrieffer-Heeger (SSH3) model is that it supports localized edge states. Although Zak's phase remains quantized for the case of a mirror-symmetric chain, it is known that it fails to take integer values in the absence of this symmetry and thus it cannot play the role of a well-defined bulk invariant in the general case. Attempts to establish a bulk-edge correspondence have been made via Green's functions or through extensions to a synthetic dimension. Here we propose a simple alternative for SSH3, utilizing the previously introduced sublattice Zak's phase, which also remains valid in the absence of mirror symmetry and for non-commensurate chains. The defined bulk quantity takes integer values, is gauge invariant, and can be interpreted as the difference of the number of edge states between a reference and a target Hamiltonian. Our derivation further predicts the exact corrections for finite open chains, is straightforwadly generalizable, and invokes a chiral-like symmetry present in this model.
