COM framework for d-wave superconductivity in the 2D Hubbard model

The two-dimensional Hubbard model has been studied within the Composite Operator Method (COM) [1] starting from a basis made of the two Hubbard composite fields in the Nambu representation and computing the residual self-energy in the non-crossing approximation (NCA) [2]. The charge-charge, spin-spin and pair-pair susceptibilities, involved in the calculation of the self-energy within NCA in the paramagnetic phase, has been computed in the two-pole approximation [1]. The analysis of the d-wave superconducting solution additionally requires the calculation of the charge-pair susceptibility. Therefore, we decided to enlarge the bosonic basis and consider a four-component composite bosonic field to be studied within a four-pole approximation. We here report, in some detail, the quite complex calculation framework and the charge-pair susceptibility in the one-loop approximation. (C) 2010 Elsevier B.V. All rights reserved.