Unifying collisional models and the Monte Carlo Metropolis method: Algorithms for dynamics of open quantum systems

Collisional models, or repeated interaction schemes, are a category of microscopic open quantum system models that have seen growing use in studying quantum thermalization, in which the bath is modeled as a large ensemble of identical ancillas that sequentially interact with the system. We demonstrate an equivalence between the system dynamics generated by the collisional model framework and the Metropolis algorithm, subject to two primary conditions. Namely, that each collisional model bath ancilla is prepared in a thermal state with a discrete spectrum that matches the energy eigenstate transitions of the system and that the ratio of the ancilla partition function to the number of system eigenstates remains small. If these conditions are satisfied, then the system dynamics generated by both methods are identical for arbitrary initial states and in both the steady-state and transient regimes. This allows the typically purely phenomenological Metropolis scheme to be used as a tool to study exact prethermalization dynamics without the need to explicitly model the system-bath interaction.