Many-body quantum state di(cid:11)usion for non-Markovian dynamics in strongly interacting systems

Capturing non-Markovian dynamics of open quantum systems is generally a challenging problem, especially for strongly-interacting many-body systems. In this work, we combine recently developed non-Markovian quantum state di(cid:11)usion techniques with tensor network methods to address this challenge. As a (cid:12)rst example, we explore a Hubbard-Holstein model with dissipative phonon modes, where this new approach allows us to quantitatively assess how correlations spread in the presence of non-Markovian dissipation in a 1D many-body system. We (cid:12)nd regimes where correlation growth can be enhanced by these e(cid:11)ects, o(cid:11)ering new routes for dissipatively enhancing transport and correlation spreading, relevant for both solid state and cold atom experiments. This supplementary material gathers numerical details and additional information about the results presented in the main text. In Sec. I we provide more details on HOPS and how it is used in practice. In Sec. II, we present a numerical benchmarking of the hybridized HOPS + MPS algorithm. In Sec. III, we show how we generate the stochastic processes appearing in the HOPS Eqs. (3) and (6) of the main text. In Sec. IV, we present a simple Markovian master equation for the Hubbard system only. Finally, in Sec. V, we discuss how to extract the time-dependent dynamics of the environment from the algorithm.