Nanoscale physics
Properties of renormalized spectra of localized quasiparticles interacting with single- and two-mode phonon modes in  Davydov’s model at T = 0K
Tkach M.V., Hutiv V.V., Seti Ju.O., Voitsekhivska O.M.
Department of Theoretical Physics and Computer Simulation, Yuriy Fedkovych Chernivtsi National University,2, Kotsyubinsky Str., Chernivtsi-58012, Ukraine,
E-mail: hutiv. vasyl@chnu. edu. ua.

The rapid development of nanophysics has significantly activated the theory describing interaction between systems of multiband (multilevel) quasiparticles and multimode phonons. Such phenomena are important, in particular, for the understanding of the physical processes in nanoheterostructures, which are the main structural elements of quantum cascade lasers and detectors operating in infrared range.
It is well known that the methods of quantum field theory are used to calculate the renormalized spectra of interacting systems. However, the universality of these approaches unfortunately does not eliminate the known mathematical problems that arise when solving specific problems. As a result, the consistent theory of renormalized spectra of systems of quasiparticles interacting with multimode phonons is still absent. 
In the proposed paper, using a relatively simple Davydov’s model, which describes the interaction of a localized quasiparticle with non-dispersive single- and two-mode phonons and phenomenological decay at T = 0K, we, for the first time, accurately calculated and analyzed the properties of renormalized spectrum of the system where the wide region of energies contains ground state and phonon satellite states. The method of unitary transformation, which is used to calculate the Fourier image of the retarded Green's function, can be generalized for the case of the systems with an arbitrary number of phonon modes.
The revealed features of the renormalized spectrum of the system can be useful for the development of an appropriate theory for a more complicated model.

1.	Tkach M., Seti Ju.O., Voitsekhivska O.M. Diagram technique in Green’s function method for the quasiparticles interacting with phonons. Chernivtsi: Chernivtsi National University. – 2019. – 164 p. 
2.	Tkach M., Seti Ju.O., Hutiv V., Voitsekhivska O.M. Spectrum of localized quasiparticle renormalized due to the interaction with three-mode phonons. // NANO-2020, Lviv Polytechnic National University, 26-29 August.