The superconducting gap in the two-dimensional Hubbard model

Electronic spectrum and superconductivity in Hubbard model

“…To obtain a closed system of equations, we must evaluate the multiparticle GF in self-energy operator (16); this describes the processes of inelastic scattering of electrons (holes) on charge and spin fluctuations due to kinematic interaction.…”

“…The same anomalous pair correlation functions (20) were obtained in MFA for the original Hubbard model (1) in [15][16][17]. To calculate the anomalous correlation function c i↓ c i↑ N j in [15,17] the Roth procedure was used based on a decoupling of the operators on the same lattice site in the time-dependent correlation function: c i↓ (t)|c i↑ (t )N j (t ) .…”

“…However, the decoupling of the Hubbard operators on the same lattice site is not unique (as has been really observed in [15,17]) and unreliable. To escape uncontrollable decoupling, in [16] kinematical restrictions imposed on the correlation functions for the Hubbard operators were used which, however, also have not produced a unique solution for superconducting equations.…”

“…There are several later studies of superconductivity in the Hubbard model within the MFA [15][16][17], where, however, a spin-fluctuation channel of superconducting pairing resulting from the anomalous component of the self-energy was not taken into account. Electronic spectra for the effective p-d Hubbard model in MFA was calculated in [18], while self-energy effects on electronic spectra were studied in [19] based on a self-consistent solution of the Dyson equations for GFs and the self-energy.…”

A theory of superconductivity in cuprates

“…The same anomalous correlation functions were obtained in MFA for the original Hubbard model in [13][14][15]. To calculate the anomalous correlation function c i↓ c i↑ N j in [13,15] the Roth procedure was applied based on a decoupling of the operators on the same lattice site in the time-dependent correlation function: c i↓ (t)|c i↑ (t )N j (t ) .…”