Spin gap and superconductivity in the three-dimensional attractive Hubbard model

TL;DR

This study maps the phase diagram of the three-dimensional attractive Hubbard model using Monte Carlo simulations, identifying critical temperatures, crossover points, and pair formation thresholds relevant to understanding high-temperature superconductivity.

Contribution

It provides the first detailed Monte Carlo analysis of the phase diagram for the 3D attractive Hubbard model, including critical and crossover temperatures, and their dependence on doping and interaction strength.

Findings

Maximum critical temperature near filling 0.9 independent of U

Identification of a crossover temperature separating metallic and spin-gap states

Existence of a critical U for pair formation, unaffected by doping

Abstract

We study the phase diagram for the attractive ({\it i.e.,} negative-$U$) Hubbard model on a simple cubic lattice, through Monte Carlo simulations. We obtain the critical temperature, $T_c$, for superconductivity from a finite-size scaling analysis of the data for the pairing correlations. For fixed on-site attraction, $U$, $T_c$ displays a maximum near the filling factor 0.9, roughly independent of $U$. For fixed filling we estimate the crossover temperature $T^\times(U)$, separating the normal states: metallic and spin-gap. There is also a critical value $U_p$ for pair formation, the magnitude of which seems to be independent of doping. The relevance of these results to the high-$T_c$ oxides is discussed.