Method of successive separation and summing of multiplicative diagrams of mass operator for the multi-level quasiparticle interacting with polarization phonons

TL;DR

This paper introduces a new diagrammatic method for calculating the energy spectrum of multi-level quasiparticles interacting with phonons, revealing significant spectral changes due to interlevel interactions and phonon complexes.

Contribution

A novel approach using successive separation and summation of diagrams for the mass operator in quasiparticle-phonon interactions, enhancing understanding of multi-phonon processes.

Findings

Interlevel phonon interactions significantly alter the spectrum.

Formation of quasi-equidistant phonon satellite bands near threshold energies.

Effective summation of diagrams as branched chain fractions.

Abstract

The theory of renormalized energy spectrum of a multi-level quasiparticle interacting with polarization phonons at $T=0$ K is developed within the Feynman-Pines diagram technique in a new approach. It permits a successive separation of multiplicative diagrams from non-multiplicative ones for all orders of mass operator, and their partial summing as well. The obtained mass operator is presented as a sum of branched chain fractions, which effectively take into account the multi-phonon processes. For the two-level quasiparticle it is shown that just the interlevel (non-diagonal) interaction with phonons fundamentally changes the properties of the spectrum. In the vicinity of all threshold energies, the quasi-equidistant phonon satellite bands (i.e., groups of energy levels) are formed. They correspond to the complexes of bound states of a quasi-particle with many phonons.