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The behavior of the 1D Holstein polaron is described, with emphasis on lattice coarsening effects, by distinguishing between adiabatic and nonadiabatic contributions to the local correlations and dispersion properties. The original and unifying systematization of the crossovers between the different polaron behaviors, usually considered in the literature, is obtained in terms of quantum to classical, weak coupling to strong coupling, adiabatic to nonadiabatic, itinerant to self-trapped polarons and large to small polarons. It is argued that the relationship between various aspects of polaron states can be specified by five regimes: the weak-coupling regime, the regime of large adiabatic polarons, the regime of small adiabatic polarons, the regime of small nonadiabatic (Lang-Firsov) polarons, and the transitory regime of small pinned polarons for which the adiabatic and nonadiabatic contributions are inextricably mixed in the polaron dispersion properties. The crossovers between these five regimes are positioned in the parameter space of the Holstein Hamiltonian. [ABSTRACT FROM AUTHOR]

The translationally invariant diagrammatic quantum perturbation theory (TPT) is applied to the polaron problem on the 1D lattice, modeled through the Holstein Hamiltonian with the phonon frequency ω0, the electron hopping t and the electron-phonon coupling constant g. The self-energy diagrams of the fourth-order in g are calculated exactly for an intermittently added electron, in addition to the previously known second-order term. The corresponding quadratic and quartic corrections to the polaron ground state energy become comparable at t/ω0>1 for g/ω0∼(t/ω0) 1/4 when the electron self-trapping and translation become adiabatic. The corresponding non adiabatic/adiabatic crossover occurs while the polaron width is large, i.e. the lattice coarsening negligible. This result is extended to the range (t/ω0)1/2>g/ω0>(t/ω0)1/4>1 by considering the scaling properties of the high-order self-energy diagrams. It is shown that the polaron ground state energy, its width and the effective mass agree with the results found traditionally from the broken symmetry side, kinematic corrections included. The Landau self-trapping of the electron in the classic self-consistent, localized displacement potential, the restoration of the translational symmetry by the classic translational Goldstone mode and the quantization of the polaronic translational coordinate are thus all encompassed by a quantum theory which is translationally invariant from the outset. This represents the first example, open to various generalizations, of the capability of TPT to hold through the adiabatic symmetry breaking crossover. Plausible arguments are also given that TPT can describe the g/ω0>(t/ω0)1/2 regime of the small polaron with adiabatic or non-adiabatic translation, i.e., that TPT can cover the whole g/ω0, t/ω0 parameter space of the Holstein Hamiltonian. [ABSTRACT FROM AUTHOR]

We study the effect of antiferromagnetic (AF) correlations in the three-band Emery model, with respect to the experimental situation in weakly underdoped and optimally doped BSCCO. In the vicinity of the vH singularity of the conduction band there appears a central peak in the middle of a pseudogap, which is in an antiadiabatic regime, insensitive to the time scale of the mechanism responsible for the pseudogap. We find a quantum low-temperature regime corresponding to experiment, in which the pseudogap is created by zero-point motion of the magnons, as opposed to the usual semiclassical derivation, where it is due to a divergence of the magnon occupation number. Detailed analysis of the spectral functions along the (π,0)–(π,π) line show significant agreement with experiment, both qualitative and, in the principal scales, quantitative. The observed slight approaching-then-receding of both the wide and narrow peaks with respect to the Fermi energy is also reproduced. We conclude that optimally doped BSCCO has a well-developed pseudogap of the order of 1000 K. This is only masked by the narrow antiadiabatic peak, which provides a small energy scale, unrelated to the AF scale, and primarily controlled by the position of the chemical potential. [ABSTRACT FROM AUTHOR]