On topological Anderson insulators : from SDRG to machine learning

This thesis is about topological Anderson insulators. It is divided into two parts: one in which we study the so-called Strong Disorder Renormalization Group (SDRG) analysis of a disordered wire, and other in which we use a Neural Network that can recognize topological phases in clean insulators, with possibility of extension to disordered insulators. In the ?rst part, we start with a review of the basic concepts about Anderson localization and one of the most known models for topological insulators (named the Su-Schriefer-Heeger - SSH - model). Then, we study a disordered wire with chiral symmetry, considering that the usual single parameter scaling hypothesis is violated, and introducing a second scaling parameter. Using the SDRG analysis, we show how to obtain the two-parameter ?ow diagram for this model. The second part, in its turn, addresses a brief picture to what is a Machine Learning algorithm and more precisely, one with a Feed-forward Neural Network (FNN) architecture. Our starting point is the question of how Machine Learning can be useful to classify topological phases of matter. We found the phase diagram of a clean insulator and extend the analysis for a disordered insulator.