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 Rényi negativity (Formula presented.) is used, which reduces to the third Rényi 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.