Some Global Properties of the Attractive Hubbard Model in the Superconducting Phase: T-Matrix Approximation in 2D

TL;DR

This paper uses the T-matrix approximation and FFT to analyze the 2D attractive Hubbard model below the critical temperature, revealing deviations from traditional BCS theory in global properties.

Contribution

It extends previous calculations by efficiently solving self-consistent T-matrix equations using FFT to explore the model's properties.

Findings

Calculated $T_c$ as a function of electron density and interaction strength

Found significant deviations from BCS behavior in global properties

Extended previous computational methods for the model

Abstract

We have applied the Fast Fourier transform (FFT), which allows to compute efficiently convolution sums, to solve the set of self-consistent T-matrix equations to get the Green function of the two dimensional attractive-U Hubbard modelbelow $T_c$, extending previous calculations of the same authors. Using a constant order parameter $\Delta(T)$, we calculated $T_c$ as a function of electron density and interaction strength $U$. These global results deviate from the BCS behavior remarkably.