  The fundamental link between entanglement dynamics and non-equilibrium statistics in isolated quantum systems has been established in theory and confirmed via experiment. However, the understanding of several consequential phenomena, such as the Many-Body Localization (MBL), has been obstructed by the lack of a systematic approach to obtain many-body entanglement dynamics. This paper introduces the Quantum Correlation Transfer Function (QCTF) approach to entanglement dynamics in many-body quantum systems and employs this new framework to demonstrate the mechanism of MBL in disordered spin chains. We show that in the QCTF framework, the entanglement dynamics of two-level constituent particles of a many-body quantum system can be fully characterized directly from the system's Hamiltonian, which circumvents the bottleneck of calculating the many-body system's time-evolution. By employing the QCTF-based approach to entanglement dynamics, we demonstrate MBL dynamics in disordered Heisenberg spin chains through the suppressed quasi-periodic spin's entanglement evolution after a quench from an anti-ferromagnetic state. Furthermore, we prove the validity of a previous fundamental conjecture regarding the MBL phase by showing that in strongly-disordered spin chains with short-range interactions, the quantum correlation between particles is exponentially attenuated with respect to the site-to-site distance. Moreover, we obtain the lowest possible amplitude of the quasi-periodic spin's entanglement as a function of disorder in the chain. The QCTF analysis is verified by exact numerical simulation of the system's evolution. We also show that QCTF provides a new foundation to study the Eigenstate Thermalization Hypothesis (ETH). The QCTF methodology can be extended in various ways to address general issues regarding non-equilibrium quantum thermodynamics in spin lattices with different geometries. 
Directly Revealing Entanglement Dynamics through Quantum Correlation   Transfer Functions with Resultant Demonstration of the Mechanism of Many-Body   Localization