This book analyzes a huge variety of exotic properties of quasi-one-dimensional topological insulators. This is preceded by an in-depth introduction about topological insulators that
presents these quantum materials in several increasing levels of depth and using various approaches like geometric phases, Berry magnetism, symmetry indicators and holonomy. After this preamble, the thesis goes on to study the Creutz ladder, a rich quasi-1D topological model that presents some exotic properties like flat bands, hidden symmetries, protecting particle-hole symmetries and a range of different topological edge states. We also study other related models with more unusual kinds of topological features, like square-root topology or tunable symmetries. Finally, we investigate the use of topological domain walls in several 1D topological insulators in order to speed-up and improve the performance of transfer protocols between their boundaries. We study their robustness against disorder and their applications in the field of entanglement distribution, proposing a protocol to create maximally entangled multipartite states.
