Interacting and Dynamical Properties of Su-Schrieffer-Heeger like Systems

Abstract

© 2025 Anirban GhoshTopological phases constitute an important aspect of modern condensed matter physics, and the Su-Schrieffer-Heeger (SSH) model is one of the most simple ways to construct such a system. As a result, it remains one of the most heavily applied/studied systems across classical and quantum settings. Two important aspects of this model are that it is essentially a single particle and hosts robust edge states in certain regions of parameter space, but it does not in other regions. These attributes have intrigued interest in a couple of directions, and among these, one is the effect of interactions on the topology of the system. Another such direction is the dynamics of the topological edge state in response to that of the quantum quench. In this thesis, we present our work in these two directions. Starting from the core concepts, we examine the non-equilibrium dynamics of an extended SSH model under quantum quenches across topological phases, unveiling the role of path of winding number transitions in shaping information transport. We then introduce complex impurities into the SSH system, demonstrating the emergence of asymmetric post-quench transport, where reflection asymmetry undergoes polarity switching with increasing quench extent. Finally, we investigate how interactions modify the topological edge states of a bosonic SSH system, employing an interacting continuum Dirac equation approach and a novel algorithm to extract boundary states in the presence of interactions. This then motivates an investigation of topological edge states in a 1D interacting ultra cold Bose gas in a periodic potential using the Gross-Pitaevskii equation, employing the algorithm. Overall, these studies provide insight into the fate of the edge states with respect to quenching and interactions