Spectrum of a two-level quasiparticle renormalized by interaction with polarization phonons at weak interlevel coupling

Abstract

For a system of the two-level quasiparticle interacting with polarization phonons at low temperature, using the Feynman-Pines diagrammatic technique in the two-phonon approximation under weak interlevel coupling, the mass operator and the Fourier image of the Green's function have been analytically calculated, which made possible to obtain the energy spectrum and average numbers of phonons in all states of the system. It has been revealed that the interaction with phonons results in a low-energy shift of both quasiparticle states and the appearance of complexes of satellite states in the spectrum. The calculation of the average numbers of phonons testified that (i) the first ground state possesses only quasiparticle properties; (ii) the properties of the second ground state depend on the distance to the first state and can be either quasiparticle-like, hybrid, or phonon-like; (iii) all satellite states are only hybrid or phonon-like.