Periodically refreshed baths to simulate open quantum many-body dynamics

We acknowledge support from the European Research Council Starting Grant ODYSSEY (Grant No. G. A. 758403), the SFI-Royal Society University Research Fellowship scheme. S.C. acknowledges the Science Foundation Ireland Starting Investigator Research Grant SpeedDemon (Grant No. 18/SIRG/5508). A.P. acknowledges funding from European Unions Horizon 2020 research and innovation program under the H2020 Marie Sklodowska-Curie Actions Grant Agreement No. 890884. A.P. acknowledges the Irish Centre for High End Computing (ICHEC) for the provision of computational facilities. G.G. acknowledges support from FQXi Grant No. DFG FOR2724. J.P. is grateful for financial support from Ministerio de Ciencia, Innovacion y Universidades (SPAIN), including FEDER (Grant No. PGC2018-097328-B100) together with Fundacion Seneca (Murcia, Spain) (Project No. 19882/GERM/15). A.P. thanks Gerald Fux for useful discussions. We also thank an anonymous referee for extremely insightful suggestions which helped improve the paper manifold.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 is due to a combination of the prevalence of strong correlations in the system, the infinite nature of the baths and the long time to reach steady state. In this paper, we develop a general formalism that allows access to the full non-Markovian dynamics of such open quantum many-body systems up to the nonequilibrium steady state, provided its uniqueness. Specifically, we show how finite-time evolution in the presence of finite-sized baths, whose opportune size is determined by their original spectral density, can be recursively used to faithfully reconstruct the exact dynamics without requiring any small parameter. Such a reconstruction is possible even in parameter regimes which would otherwise be inaccessible by current state-of-the-art techniques. We specifically demonstrate this by obtaining the full numerically exact non-Markovian dynamics of interacting fermionic chains in two terminal setups with finite temperature and voltage biases, a problem which previously remained outstanding despite its relevance in a wide range of contexts, for example, quantum heat engines and refrigerators.European Research Council Starting Grant ODYSSEY G. A. 758403SFI-Royal Society University Research Fellowship schemeScience Foundation Ireland European Commission 18/SIRG/5508European Unions Horizon 2020 research and innovation program under the H2020 Marie Sklodowska-Curie Actions Grant 890884FQXi DFG FOR2724Ministerio de Ciencia, Innovacion y Universidades (SPAIN)Fundacion Seneca 19882/GERM/15European Commission PGC2018-097328-B10