Localization-delocalization transition of a polaron near an impurity

We solve the problem of polaron localization on an attractive impurity by means of direct-space Diagrammatic Monte Carlo implemented for the system in the thermodynamic limit. In particular we determine the ground state phase diagram in dependence on the electron-phonon coupling and impurity potential strength for the whole phonon frequency range. Including the quantum phonon dynamics we find and characterize a new phase which is missing in the zero phonon-frequency limit (adiabatic approximation), where self-trapped polarons are not localized at shallow impurities. We predict and show that in the vicinity of the localization transition a region with a mixture of weak- and strong-coupling spectral response is realized.