Dynamics of Negativity of a Wannier-Stark Many-Body Localized System Coupled to a Bath

An interacting system subjected to a strong linear potential can host a many-body localized (MBL) phase when being slightly perturbed. This so-called Wannier-Stark or "tilted-field" MBL phase inherits many properties from the well-investigated disordered MBL phase, and provides an alternative route to experimentally engineer interacting localized systems without quenched disorder. Herein, the dynamics of entanglement in a Wannier-Stark MBL system coupled to a dephasing environment is investigated. As an accessible entanglement proxy, the third Renyi negativity R 3 is used, which reduces to the third Renyi entropy in case the system is isolated from the environment. This measure captures the characteristic logarithmic growth of interacting localized phases in the intermediate-time regime, where the effects of the coupling to the environment are not yet dominating the dynamics. Thus, it forms a tool to distinguish Wannier-Stark MBL from noninteracting Wannier-Stark localization up to intermediate time-scales, and to quantify quantum correlations in mixed-state dynamics.