Directly Obtaining Entanglement Dynamics through Quantum Correlation Transfer Functions; Demonstrating the Mechanism of Many-Body Localization

We introduce the Quantum Correlation Transfer Function (QCTF) approach to entanglement dynamics in many-body quantum systems and employ this framework to demonstrate the mechanism of Many-Body Localization (MBL). We show that in the QCTF framework, the entanglement dynamics of the two-level 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. This result provides a new foundation to study the Eigenstate Thermalization Hypothesis (ETH). By employing the QCTF-based approach, we demonstrate the MBL dynamics in disordered Heisenberg spin chains. 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 interaction, the quantum correlation between particles is exponentially attenuated with respect to the site-to-site distance. The QCTF approach can be extended to address general issues regarding non-equilibrium quantum statistics in spin lattices with different geometries.