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The fundamental link between entanglement dynamics and non-equilibriumstatistics in isolated quantum systems has been established in theory andconfirmed via experiment. However, the understanding of several consequentialphenomena, such as the Many-Body Localization (MBL), has been obstructed by thelack of a systematic approach to obtain many-body entanglement dynamics. Thispaper introduces the Quantum Correlation Transfer Function (QCTF) approach toentanglement dynamics in many-body quantum systems and employs this newframework to demonstrate the mechanism of MBL in disordered spin chains. Weshow that in the QCTF framework, the entanglement dynamics of two-levelconstituent particles of a many-body quantum system can be fully characterizeddirectly from the system's Hamiltonian, which circumvents the bottleneck ofcalculating the many-body system's time-evolution. By employing the QCTF-basedapproach to entanglement dynamics, we demonstrate MBL dynamics in disorderedHeisenberg spin chains through the suppressed quasi-periodic spin'sentanglement evolution after a quench from an anti-ferromagnetic state.Furthermore, we prove the validity of a previous fundamental conjectureregarding the MBL phase by showing that in strongly-disordered spin chains withshort-range interactions, the quantum correlation between particles isexponentially attenuated with respect to the site-to-site distance. Moreover,we obtain the lowest possible amplitude of the quasi-periodic spin'sentanglement as a function of disorder in the chain. The QCTF analysis isverified by exact numerical simulation of the system's evolution. We also showthat QCTF provides a new foundation to study the Eigenstate ThermalizationHypothesis (ETH). The QCTF methodology can be extended in various ways toaddress general issues regarding non-equilibrium quantum thermodynamics in spinlattices with different geometries.

Directly Revealing Entanglement Dynamics through Quantum Correlation  Transfer Functions with Resultant Demonstration of the Mechanism of Many-Body  Localization