Green’s function of the Holstein polaron

Abstract

We present a novel, highly efficient yet accurate analytical approximation for the Green's function of a Holstein polaron. It is obtained by summing all the self-energy diagrams, but with each selfenergy diagram averaged over the momenta of its free propagators. The result becomes exact for both zero bandwidth and for zero electron-phonon coupling, and is accurate everywhere in the parameter space. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Comparison with existing numerical data also confirms this accuracy. We use this approximation to analyze in detail the redistribution of the spectral weight as the coupling strength varies.

Single-polaron properties of the one-dimensional breathing-mode Hamiltonian

“…Similar to the Holstein model, the large-to-small polaron transition occurs at lower λ for increasing α. 23,38 At weak and moderate coupling, the qp weight and the effective mass (not shown) in the breathing-mode model are much less sensitive to an increase in α, than is the case for the Holstein polaron. This suggests that breathing-mode polarons should be better charge carriers than the Holstein polarons, in this regime.…”

“…In 1D we can investigate accurately and efficiently not only ground-state (GS) properties, but also some excited state properties. For the Holstein model, it was found that polaron properties are qualitatively similar in different dimensions, 23,38 but with a sharper large-to-small polaron crossover in higher dimensions. We will show that a sharp crossover is already present in the 1D model, and we expect less dimensionality effects in the breathing-mode Hamiltonian.…”

“…30−35 Analytic approximations have also progressed over the years. 36,37,38,39 For some materials, a more appropriate model is provided by the breathing-mode Hamiltonian. For example, consider a half-filled 2D copper-oxygen plane of a parent cuprate compound.…”

Going beyond the linear approximation in describing electron-phonon coupling: Relevance for the Holstein model

“…-We use the momentum average (MA) approximation to carry out this study. MA was shown to be very accurate in describing GS polaron properties for the linear Holstein model, where it satisfies exactly multiple sum rules and becomes asymptotically exact in the limit of strong coupling [14]. It is straightforward to verify that all these considerations remain valid for the generalized Holstein model: H = H el + H ph + H el-ph , defined as follows.…”

“…From this we can extract all the polaron's GS properties [14]. We rewrite the quadratic Hamiltonian as…”