Holstein polaron: the effect of multiple phonon modes

Abstract

We generalize the Momentum Average approximations MA${}^{(0)}$ and MA${}^{(1)}$ to study the effects of coupling to multiple optical phonons on the properties of a Holstein polaron. As for a single phonon mode, these approximations are numerically very efficient. They become exact for very weak or very strong couplings, and are highly accurate in the intermediate regimes, {\em e.g.} the spectral weights obey exactly the first six, respectively eight, sum rules. Our results show that the effect on ground-state properties is cumulative in nature. In particular, if the effective coupling to one mode is much larger than to the others, this mode effectively determines the GS properties. However, even very weak coupling to a second phonon mode has important non-perturbational effects on the higher energy spectrum, in particular on the dispersion and the phonon statistics of the polaron band.

References in corpus (5)

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• Missing Quasiparticles and the Chemical Potential Puzzle in the Doping Evolution of the Cuprate Superconductors
• Green's function of a dressed particle
• The Green's Function of the Holstein Polaron
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Cited by in corpus (9)

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• Holstein polaron in the presence of disorder
• Numerically Exact Generalized Green's Function Cluster Expansions for Electron-Phonon Problems
• Beyond the single-site approximation modeling of electron-phonon coupling effects on resonant inelastic X-ray scattering spectra
• Linear rotor in an ideal Bose gas near the threshold for binding
• Renormalized spectrum of quasiparticle in limited number of states, strongly interacting with two-mode polarization phonons at $T=0$ K
• Energy flow during relaxation in an electron-phonon system with multiple modes: A nonequilibrium Green's function study