The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle–hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.
The electronic states of the two-dimensional Hubbard model are investigated by means of a 4-pole approximation within the composite operator method. In addition to the conventional Hubbard operators, we consider other two operators which come from the hierarchy of the equations of motion and carry information regarding nearest-neighbor spin and charge configurations. By means of this operatorial basis, we can study the physics related to the energy scale of
J=4t2∕U in addition to the one of
U. Present results show relevant physical features, well beyond those previously obtained by means of a 2-pole approximation, such as a four-band structure with shadow bands and a quasiparticle peak at the Fermi level. The Fermi level stays pinned to the band flatness located at $(\ensuremath{\pi},0)$-point within a wide range of hole-doping $(0\ensuremath{\leqslant}\ensuremath{\delta}\ensuremath{\leqslant}0.15)$. A comprehensive analysis of double occupancy, internal energy, specific heat and entropy features have also been performed. All reported results are in excellent agreement with the data of numerical simulations.