Simulating the dynamics of large many-body quantum systems with Schr\"odinger-Feynman techniques

The development of powerful numerical techniques has drastically improved our understanding of quantum matter out of equilibrium. Inspired by recent progress in the area of noisy intermediate-scale quantum devices, this paper highlights hybrid Schr\"odinger-Feynman techniques as an innovative approach to efficiently simulate certain aspects of many-body quantum dynamics on classical computers. To this end, we explore the nonequilibrium dynamics of two large subsystems, which interact sporadically in time, but otherwise evolve independently from each other. We consider subsystems with tunable disorder strength, relevant in the context of many-body localization, where one subsystem can act as a bath for the other. Importantly, studying the full interacting system, we observe that signatures of thermalization are enhanced compared to the reference case of having two independent subsystems. Notably, with the here proposed Schr\"odinger-Feynman method, we are able to simulate the pure-state survival probability in systems significantly larger than accessible by standard sparse-matrix techniques.