Spectral Theory of Non-Markovian Dissipative Phase Transitions

To date, dissipative phase transitions (DPTs) have mostly been studied for
quantum systems coupled to idealized Markovian (memoryless) environments, where
the closing of the Liouvillian gap constitutes a hallmark. Here, we extend the
spectral theory of DPTs to arbitrary non-Markovian systems and present a
general and systematic method to extract their signatures, which is fundamental
for the understanding of realistic materials and experiments such as in the
solid-state, cold atoms, cavity or circuit QED. We first illustrate our theory
to show how memory effects can be used as a resource to control phase
boundaries in a model exhibiting a first-order DPT, and then demonstrate the
power of the method by capturing all features of a challenging second-order DPT
in a two-mode Dicke model for which previous attempts had fail up to now.