topological invariants and anomalies in strongly correlated systems

We examine how strong correlations modify quantum anomalies in associated theories, with implications for topological phases. Quantum anomalies arise as intrinsic properties of quantum systems, often described by the Atiyah-Singer index theorem in weakly correlated cases. For strongly correlated systems, however, interaction effects necessitate a revision of this framework. We calculate the modifications to the Dirac operator induced by interactions and determine their impact on the anomalous contributions to the effective theory. The derived expressions for these interaction-driven anomalies yield insights into their role within correlated topological phases. Collectively, this work provides a new framework for defining topological invariants in strongly correlated systems and explores the fundamental modifications of quantum anomalies due to electron interactions, advancing the theoretical foundation of topological condensed matter systems.