Abstract
A microscopic theory of electronic spectrum and superconducting pairing within the Hubbard model is formulated. The Dyson equation for the normal and anomalous Green functions in terms of the Hubbard operators is derived by applying the Mori-type projection technique. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge uctuations induced by kinematic interaction for Hubbard operators. Numerical results for electron dispersion in the strong correlation limit are presented. Superconducting pairing mediated by antiferromagnetic exchange and spin uctuations is discussed.
Highlights
One of the basic models for the study of electronic spectra and superconductivity in strongly correlated electronic systems, such as the cuprate high-temperature superconductors, is the Hubbard model [1]
A rigorous analytical method is based on the Hubbard operator (HO) technique [9] since in this representation the local constraint of no double occupancy of any lattice site is rigorously implemented by the Hubbard operator algebra
Fermi-like excitations described by operators Xj = Xj0σ (Xjσ2) and Bose-like excitations described by operators Bi (8) in multiparticle Green functions (GFs) (16) are considered to propagate independently, and their correlation functions at noncoincident lattice sites (i = j, l = m) factor into a product of the corresponding functions: Bi(t)Xj (t)Bl(t )Xm(t ) Xj (t)Xm(t ) Bi(t)Bl(t )
Summary
One of the basic models for the study of electronic spectra and superconductivity in strongly correlated electronic systems, such as the cuprate high-temperature superconductors, is the Hubbard model [1]. A superconducting pairing due to the kinematic interaction in the Hubbard model in the limit of strong electron correlations (U → ∞) was first obtained by Zaitsev and Ivanov [10] who studied the two-particle vertex equation by applying a diagram technique for Hubbard operators. Superconducting pairing in the Hubbard model was studied by Plakida and Stasyuk [11] by applying the equation of motion method to the thermodynamic Green functions (GFs) [12] They have used a decoupling procedure for higher order GFs in MFA and obtained the results similar to [10] but with a different dependence of the superconducting temperature Tc(n) on the electron occupations numbers n.
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