In this talk, I will explore the interplay of interactions and disorder in topological quantum systems, focusing on both their influence on the system’s properties and the eventual breakdown of topological phases. I will first discuss how these factors modify the system’s behavior before its collapse, highlighting the emergence of prominent surface collective modes, which serve as experimental signatures of non-trivial topology, and spatially dependent order parameters. While topological systems are inherently resilient to disorder and interactions, I will examine the conditions under which these phases break down, delineating the boundaries of their stability. In particular, I will analyze how disorder and strong interactions influence the density of states, leading to the destruction of topological surface modes, often through a cascade process where higher-order topological phases vanish first. Both mean-field and beyond mean-field approaches will be discussed, highlighting universal and non-universal features. These insights offer a comprehensive view of the resilience and ultimate breakdown of topological phases under external perturbations.
Laboratory for Theoretical and Computational Physics