# Rigorous derivation of the mean field Green functions of the two-band Hubbard model of superconductivity

## TL;DR

This paper rigorously derives the mean field Green functions for the two-band Hubbard model of high-temperature superconductivity, emphasizing the algebraic invariance properties of Hubbard operators to improve the theoretical framework.

## Contribution

It introduces a rigorous derivation of Green functions using invariance properties of Hubbard operator algebra, simplifying the effective two-band Hubbard model analysis.

## Key findings

- Derived simplified expressions for Green functions
- Identified invariance properties of correlation functions
- Reduced correlation order to mean field approximation

## Abstract

The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T_c superconductivity in cuprates [N.M. Plakida et al., Phys. Rev. B, v. 51, 16599 (1995); JETP, v. 97, 331 (2003)] rests on the Hubbard operator (HO) algebra. We show that, if we take into account the invariance to translations and spin reversal, the HO algebra results in invariance properties of several specific correlation functions. The use of these properties allows rigorous derivation and simplification of the expressions of the frequency matrix (FM) and of the generalized mean field approximation (GMFA) Green functions (GFs) of the model. For the normal singlet hopping and anomalous exchange pairing correlation functions which enter the FM and GMFA-GFs, an approximation procedure based on the identification and elimination of exponentially small quantities is described. It secures the reduction of the correlation order to GMFA-GF expressions.