Properties and temperature evolution of the spectrum of localized quasi-particles interacting with polarization phonons in two models

TL;DR

This paper uses the Feynman-Pines diagram technique to analyze the energy spectrum of localized quasi-particles interacting with polarization phonons at finite temperature, revealing new bound states and the effects of multi-phonon processes.

Contribution

It introduces a comprehensive model that predicts new bound states and analyzes their behavior depending on coupling strength and temperature, extending previous simplified models.

Findings

New bound states appear even with weak coupling.

Multi-phonon processes significantly influence the spectrum.

Bound states' existence varies with temperature and coupling.

Abstract

Using the Feynman-Pines diagram technique, the energy spectrum of localized quasi-particles interacting with polarization phonons is calculated and analyzed in the wide range of energies at the finite temperature of the system. It is established that the general model of the system, besides the bound states known from the simplified model with an additional condition for the operator of quasi-particles number, contains the new bound states even for the systems with weak coupling. The contribution of multi-phonon processes into the formation of renormalized spectrum of the system is analyzed. The reasons of the appearance, behaviour and disappearance of separate pairs of bound states depending on the coupling constant and temperature are revealed.