Obtaining dynamics of an interacting quantum many-body system connected to multiple baths initially at different, finite, temperatures and chemical potentials is a challenging problem. This I s due to both the prevalence of strong correlations in the system and the infinite nature of the baths. Here we show that it is possible to accurately simulate the dynamics a wide class of such open quantum many-body systems with finite and rather small-sized baths, when the baths are refreshed to their original initial states periodically after a carefully chosen time interval. We show how this method, when combined with tensor network techniques, significantly simplifies the dynamics by allowing a continuous time non-Markovian dynamics to be mapped to a discrete time Markov process. We call this method: Periodically Refreshed Baths (PReB). We demonstrate that this method provides relatively easy access to numerically exact non-Markovian dynamics of open quantum many-body systems in parameter regimes where other numerical and analytical methods are known to struggle.
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