THE METAL-INSULATOR-TRANSITION AND FERMI-LIQUID BEHAVIOR IN THE INFINITE-DIMENSIONAL HUBBARD-MODEL

We study the Hubbard model in dimension d = infinity, within an approximation that simultaneously reproduces the atomic limit and the weak-coupling limit up to second order in the interaction strength U. This method, which is a slightly modified version of an approximation suggested by Edwards and Hertz, is applied to the calculation of the self-energy and of the spectral function in the paramagnetic regime for different U, band fillings n, and temperatures T. We find Fermi-liquid behaviour for small U and (for half-filling n = 0.5) a metal-insulator (Mott) transition at a critical value U(cr), but also a metallic non-Fermi-liquid phase for intermediate values U < U(cr). We compare our results with results obtained within the second-order perturbation theory in U and (at finite temperature) with the (essentially exact) quantum Monte Carlo (QMC) results. Qualitatively, the approximation reproduces the correct tendencies obtained by Qmc, but in detail there are still discrepancies, in particular for intermediate values of U.