The Hubbard Model in the Two-Pole Approximation

Abstract

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.

Superconductivity in a two dimensional extended Hubbard model

“…(18) and (19) will be discussed in detail in section 4. One of the most important elements of the matrix E 5 is E 24 = γ k , where…”

New Comparisons for Local Quantities of the Two-Dimensional Hubbard Model

“…The straightforward application of this scheme 8 ' [10][11][12][13] gives that, in the paramagnetic phase, J(k) has diagonal form with In = 1 -n/2 and I22 -n/2 ((n a (i)) -j) and that the m-matrix depends on three parameters: the chemical potential /x and two correlators…”

The two-dimensional t-t'-U model as a minimal model for cuprate materials

“…In the last years we have been developing a method of calculation, denominated Composite Operator Method [19][20][21][22][23][24][25] (COM), which has been revealed to be a powerful tool for the description of local and itinerant excitations in strongly correlated electronic systems. The method is based on the observation that the original field operators, in terms of which the interacting Hamiltonians are expressed, are not a convenient basis.…”

“…Unlikely other approaches, the presence of these parameters is not inconvenient because it opens the possibility to bind the dynamics in a suitable Hilbert space, reabsorbing the symmetries which might be lost when some approximations are made. In particular, by using relations with the content of the Pauli principle [19,20], we are allowed to fix the dynamics of the system in a fully selfconsistent way without recurring to factorization or other procedures [26][27][28]. In a physics dominated by the interplay between the charge and the magnetic configurations, we think that the Pauli principle should play an important role.…”

“…Furthermore, the recovery of the Pauli principle, usually violated by other approximations, assures us that the hole-particle symmetry is satisfied and that the dynamics is bound to the right Hilbert space. In fact, the symmetry dictated by the Pauli principle and that coming from the hole-particle symmetry are intimately connected, so that the violation of the former implies the violation of the latter, and vice versa [20]. In this paper, we apply the method to the t-t'-U model; preliminary results have been given in reference [29], to which we will often refer, and the study of the magnetic properties have been given in reference [22].…”