Phase diagram for the attractive Hubbard model in two dimensions in a conserving approximation

Abstract

We calculate the superconducting transition temperature as a function of interaction strength and density for a two-dimensional attractive Hubbard model in the fluctuation exchange approximation (FEA). Significant corrections to mean-field theory are apparent, including a maximum in ${T}_{c}$ as a function of U and a fluctuation-broadened specific heat peak. At $n=1,$ competing pair fluctuations and charge-density fluctuations fail to drive ${T}_{c}$ to zero. This failure of the FEA reflects an inadequate account of the coupling among fluctuations. Because ${T}_{c}$ is determined from self-consistent calculations of thermodynamic potentials, the calculations are extremely sensitive to numerical errors, requiring accuracy up to 1 part in ${10}^{6}.$ We outline a procedure for systematically reducing numerical errors associated with the finite-frequency cutoff in numerical many-body calculations such as ours.