Illustration of Key Concepts in Dimension $$d=1$$ d = 1

Abstract

This introductory chapter presents and illustrates many of the key concepts developed in this work on a simple example, namely the Su-Schriefer-Heeger model [205] of a conducting polymer. This model has a chiral symmetry and non-trivial topology, given by a non-commutative winding number which is remarkably stable against perturbations like a random potential [139]. Hence this is a relatively simple example of a topological insulator. Here the focus is on the bulk-boundary correspondence in this model, which connects the winding number to the number of edge states weighted by their chirality. This connection will be explained in a K-theoretic manner. These arguments constitute a rather mathematical introduction to the bulk-edge correspondence and the physical motivations and insights will be given in the following chapters.