Fate of entanglement in open quantum spin liquid: Time evolution of its genuine multipartite negativity upon sudden coupling to a dissipative bosonic environment

Many-body entanglement properties of quantum spin liquids (QSLs), persisting at arbitrarily long distances, have been intensely explored over the past two decades, but mostly for QSLs viewed as {\em closed} quantum systems. However, in experiments and potential quantum computing applications, candidate materials for this exotic phase of quantum matter will always interact with a dissipative environment, such as the one generated by bosonic quasiparticles in solids at finite temperature. Here we investigate both the {\em stability} and {\em spatial distribution} of entanglement for the Kitaev model of QSL, which is made {\em open} by its sudden coupling to an infinite bosonic bath of Caldeira-Leggett type and then time-evolved in both Markovian and non-Markovian regimes. From the time-dependent density matrix of QSL subregions, we extract genuine multipartite negativity (GMN), quantum Fisher information, spin-spin correlators, and the expectation value (EV) of the Wilson loop operator. In particular, time dependence of GMN offers the most penetrating insights: ({\em i}) in the Markovian regime, it remains nonzero only in hexagonal loopy subregions of QSL (as also discovered very recently for closed QSLs), eventually vanishing on the same timescale on which the EV of the Wilson loop operator vanishes; ({\em ii}) in the non-Markovian regime with pronounced memory effects, surprisingly, GMN remains nonzero up to much higher temperatures while also remaining zero in non-loopy subregions. In addition, the non-Markovian dynamics generates emergent interactions between spins, thereby opening avenues for tailoring properties of QSL via engineering of dissipation.