Energy spectrum of localized quasiparticles renormalized by multi-phonon processes at finite temperature

TL;DR

This paper develops a comprehensive theoretical framework and computational tool to analyze the energy spectrum of localized quasiparticles interacting with phonons at finite temperature, accounting for multi-phonon processes.

Contribution

It introduces a novel method to accurately compute the renormalized quasiparticle spectrum considering multi-phonon interactions and temperature effects using diagrammatic techniques.

Findings

Identification of bound state complexes at various energies.

Dependence of spectrum properties on coupling strength and temperature.

Effective separation and summation of pole and non-pole mass operator terms.

Abstract

The theory of renormalized energy spectrum of localized quasi-particle interacting with polarization phonons at finite temperature is developed within the Feynman-Pines diagram technique. The created computer program effectively takes into account multi-phonon processes, exactly defining all diagrams of mass operator together with their analytical expressions in arbitrary order over the coupling constant. Now it is possible to separate the pole and non-pole mass operator terms and perform a partial summing of their main terms. The renormalized spectrum of the system is obtained within the solution of dispersion equation in the vicinity of the main state where the high- and low-energy complexes of bound states are observed. The properties of the spectrum are analyzed depending on the coupling constant and the temperature.