Energy spectrum of electron-phonon complex states in three-level system of localized quasi-particles at low temperatures

The spectrum of three-level localized quasi-particle renormalized due to the interaction with polarization phonons is studied within the Feynman-pines diagram technique at cryogenic temperature. It is shown that in such system, besides the renormalized three main states, the complexes of bound states exist. Their properties are essentially different depending on the energetic distance between the starting levels, which are in resonance with the phonon energy or not.