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Journal of Experimental and Theoretical Physics Letters

Kinematic mechanism of the modulation of the spectral intensity in the spatially uniform system of Hubbard fermions

Valerii Vladimirovich Val'kov, A. A. Golovnya, M. M. Korovushkin

Published Oct 1, 2011• 1 citation
Publisher

Abstract

Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions leads to significant variations in the spectral intensity A ( k , ω) in the Brillouin zone. As a result, the modulation of A ( k , ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by the contour section, where A ( k , ω) decreases according to the angle-resolved photoemission spectroscopy data.

DOI
10.1134/s0021364011150148

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Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions leads to significant variations in the spectral intensity A ( k , ω) in the Brillouin zone. As a result, the modulation of A ( k , ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by the contour section, where A ( k , ω) decreases according to the angle-resolved photoemission spectroscopy data.
It is shown that the kinematic interaction caused by the quasi-Fermi character of commutation relations for operators of the atomic representation can induce pseudogap behavior of the spectral characteristics of an ensemble of Hubbard fermions. Mathematically, the presence of the kinematic interaction manifests itself in modification of the faithful representation of a single-particle Green's function of Hubbard fermions D(k,iωn)D(\textbf{k},iω_n)D(k,iωn​), which involves, apart from self-energy operator ΣL(k,iωn)Σ_L(\textbf{k},iω_n)ΣL​(k,iωn​), strength operator P(k,iωn)P(\textbf{k},iω_n)P(k,iωn​). It is important that the strength operator enters both the numerator and the denominator of the exact expression for D(k,iωn)D(\textbf{k},iω_n)D(k,iωn​). The kinematic interaction, therefore, not only renormalizes the spectrum of elementary excitations but significantly affects their spectral weight. It results in strong modulation of spectral intensity A(k,ω)A(\textbf{k},ω)A(k,ω) occurring on a Fermi contour. Calculations of the spectral properties for the t−Jt-Jt−J model in the one-loop approximation yield good quantitative agreement with the ARPES data obtained on cuprate superconductors.
The electronic structure with the spectral line broadening corresponding to the angle-resolved photoemission spectroscopy resolution has been calculated for the Hubbard model, t–J and t–J* models within the norm-conserving cluster perturbation theory. The electronic dispersion anomalies similar to the high-energy kinks observed in the angle-resolved photoemission spectroscopy experiments are obtained at the energy scale of order of the hopping integral t. The doping dependence of the high-energy anomalies for different Coulomb repulsion values is discussed. The influence of the threesite correlated hopping on the results is analyzed.
We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands, there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electron kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators, which results in the kinematic spin-fluctuation pairing mechanism for V ≲ W. The theory is based on the Mori projection technique in the equation of motion method for the Green’s functions in terms of the Hubbard operators. The doping dependence of the superconductivity temperature T c is calculated for various values of U and V.
We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electronic kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators which results in the kinematic spin-fluctuation pairing mechanism for V < W . The theory is based on the Mori projection technique in the equation of motion method for the Green functions in terms of the Hubbard operators. The doping dependence of superconductivity temperature Tc is calculated for various values of U and V.
We discuss spectra calculated for the two-dimensional Hubbard model in the intermediate coupling regime with the dynamical cluster approximation, which is a nonperturbative approach. We find a crossover from a normal Fermi liquid with a Fermi surface closed around the Brillouin-zone center at large doping to a non-Fermi liquid for small doping where the Fermi surface is holelike, closed around $M=(\ensuremath{\pi},\ensuremath{\pi}).$ The topology of the Fermi surface at low doping indicates a violation of Luttinger's theorem. We discuss different ways of presenting the spectral data to extract information about the Fermi surface. A comparison to recent experiments is presented.
Abstract We derive a general procedure for evaluating the nth derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded electronic Green’s function and self-energy for a system described by the Holstein–Hubbard model allowing for arbitrary spatial and time variation of all parameters (including spatially homogeneous electric fields and parameter quenches). For a translationally invariant (but time-dependent) Hamiltonian, we also provide sum rules in momentum space. The sum rules can be applied to various different phenomena like time-resolved angle-resolved photoemission spectroscopy and benchmarking the accuracy of numerical many-body calculations. This work also corrects some errors found in earlier work on simpler models.