Explore eigenstate correlations and information scrambling in quantum many-body systems through this 44-minute conference talk delivered at the International Centre for Theoretical Sciences. Delve into the theoretical framework connecting eigenstate properties with quantum information dynamics, examining how information spreads and becomes scrambled in complex quantum systems. Learn about the mathematical foundations underlying eigenstate correlations and their role in understanding thermalization and quantum chaos. Discover applications of these concepts to logarithmic systems and their unique properties in quantum condensed matter physics. Gain insights into cutting-edge research methodologies for analyzing quantum information flow and eigenstate structure in strongly correlated systems. This presentation forms part of the Discussion Meeting on Frontiers in Quantum Condensed Matter Physics, featuring contributions from leading researchers exploring new paradigms beyond conventional broken symmetries and quasiparticle descriptions.