Hierarchical classical metastability in an open quantum East model

We study in detail an open quantum generalisation of a classical kinetically constrained model -- the East model -- known to exhibit slow glassy dynamics stemming from a complex hierarchy of metastable states with distinct lifetimes. Using the recently introduced theory of classical metastability for open quantum systems, we show that the driven open quantum East model features a hierarchy of classical metastabilities at low temperature and weak driving field. We find that the effective long-time description of its dynamics is not only classical, but shares many properties with the classical East model, such as obeying an effective detailed balance condition, and lacking static interactions between excitations, but with this occurring within a modified set of metastable phases which are coherent, and with an effective temperature that is dependent on the coherent drive.