By Peyman Azodi

Understanding entanglement propagation in out-of-equilibrium many-body quantum systems is important for both fundamental and practical reasons, especially given the new developments regarding the interrelationship between entanglement and thermodynamics in quantum systems. However, understanding the dynamics of entanglement requires access to the exponentially large Hilbert space of the system, which is highly challenging.

In the Rabitz group, we theoretically study the entanglement dynamics in many-body quantum systems, through the Quantum Correlation Transfer Function (QCTF) formulation. In this formulation, the evolution of a quantum system is mapped to a multi-variable complex space. Hence, dynamics of subsystems’ entanglement can be obtained using techniques from complex analysis, for example, the Cauchy’s integral theorem. As a result of this transformation, entanglement between subsystems can be obtained without knowledge of the system’s state, and directly from the Hamiltonian.

QCTF has been used to study Many-Body Localization (MBL), to reveal the underlying mechanism for slow growth of entanglement in long-range interacting Heisenberg chains, and in other emergent problems in many-body quantum system’s theory.