Non-Markovian Quantum Dynamics via General Quantum Master Equation and Tensor Networks

Computing real-time dynamics of a quantum many-body system is challenging due to the exponential growth of entanglement. While many different approaches have been investigated, how to compute the real-time dynamics of generic condensed matter systems, or how to best classify for which systems the dynamics cannot feasibly be computed on a classical computer, remain open questions. In this work, we treat the Nakajima-Zwanzig general quantum master equation with tensor network methods to identify the limits of classical time evolution algorithms. Though the memory kernel is difficult to compute even numerically, tensor networks provide a systematic means of obtaining the kernel for diverse complex systems, such as the spin-boson model with anharmonic bath sites. In this work we focus on the spin-boson model and analyze how the types and strengths of interactions affect the lifetime of the memory kernel. Our work provides general insight into the classical simulatability of quantum dynamics.