Extended flat band, entanglement, and topological properties in a Creutz ladder
Yoshihito Kuno
Abstract
In this work, we study the entanglement and topological properties of an extended flat-band Creutz ladder by considering a compacted localized state (CLS). Based on the CLS picture, we find a multiple flat-band extension from the conventional two flat-band Creutz ladder. A simple vertical interchain coupling leads to a four complete flat-band system and creates an additive $\ensuremath{\pi}$-flux pattern on the Creutz ladder. Interestingly, the strong coupling induces a topological phase transition where the distribution of CLSs is modified: upper and lower flat-band CLSs are paired up. This pairing leads to the destruction of the CLS entanglement and, hence, to a vanishing edge mode (i.e., the breakdown of the nontrivial topological phase). Finally, we study the localization dynamics induced by the presence of complete flat bands in this extended flat-band system.