Approximation methods in a superconducting model

H. Matsumoto, Hiroomi Umezawa

Abstract A rigorous formulation of the boson method in superconductivity is presented. Assuming the local gauge invariance and presence of a phase‐dependent order parameter and utilizing the path‐integral formalism, we derive a set of macroscopic equations which control all the superconducting states. These equations are model‐independent. They contain certain functions and parameters which should be calculated for a given model. Using this rigorous formulation, we study what kind of approximations are involved in the usual formulation of the boson method and how these approximations can be improved.

J. R. Schrieffer

Tatiana N. Antsygina, V. A. Slyusarev

The possibility of the existence of superconducting correlations is analyzed by using the Hubbard model with repulsion on the basis of the generalized self-consistent field method (without resorting to the auxiliary field formalism or equivalent approximations based on the “spherical” type uncontrollable approximations). It is shown that a superconducting solution does not exist in this method under the condition forbidding a double occupancy of a lattice site. The results are compared with the recent data.

Gorazd Ocvirk

Anna Kauch, Felix Hörbinger, Kitatani, Motoharu +2 more

We study the Hubbard model on a square lattice, using the dynamical vertex approximation and the parquet approximation. These methods allow us to describe the mutual interference of spin-fluctuations in the particle-hole channel and superconducting fluctuations in the cooperon channel in an unbiased way. For small dopings we find predominant commensurable antiferromagnetic spin- and d-wave superconducting fluctuations; for larger doping incommensurate antiferromagnetic spin fluctuations are concomitant to triplet s-wave superconducting fluctuations.

A. Zawadowski, G. Pócsik