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arXiv:2103.15556 · Condensed Matter Physics

Renormalized spectrum of quasiparticle in limited number of states, strongly interacting with two-mode polarization phonons at T=0 K

N. V. Tkach, Julia O. Seti, Оxana Voitsekhivska

Published Mar 1, 2021• 1 citation
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Abstract

Within unitary transformed Hamiltonian of Fröhlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at T=0 K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed.

DOI
10.5488/cmp.24.13705

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Within unitary transformed Hamiltonian of Fröhlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at T=0 K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed.
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.
The theory of renormalized energy spectrum of a multi-level quasiparticle interacting with polarization phonons at T=0T=0T=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.
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.
The Fr\"ohlich model describes the interaction of a mobile impurity with a surrounding bath of phonons which leads to the formation of a quasiparticle, the polaron. In this paper an efficient renormalization group approach is presented which provides a description of Fr\"ohlich polarons in all regimes ranging from weak to strong coupling. The extended renormalization group approach introduced here is capable of predicting ground state properties for arbitrarily small impurity masses. This allows us to obtain the full phase diagram of the Fr\"ohlich Hamiltonian, which we present concretely for the Bogoliubov-Fr\"ohlich model originally introduced to describe ultracold impurities in a Bose-Einstein condensate. For this model, whose regime of validity in ultracold quantum gases is the subject of debate, we benchmark our method by comparison of the ground state energy to recent diagrammatic quantum Monte Carlo calculations.
The change of the spectral properties of the single-particle Green's function due to a coupling to optical phonons is investigated for strongly correlated electrons. The phonon-induced mass renormalization of the carriers that propagate in the t-J model on scale J is much larger than in the corresponding uncorrelated model, except in the limit of J\ensuremath{\rightarrow}0 where the weight of the quasiparticle pole tends to zero. The enhancement is a consequence of the slow coherent motion of the spin polarons, which makes electron-phonon interactions more effective. Two scaling laws are determined which relate the mass renormalization to phonon frequency and coupling constant.