The Metal-Insulator Transition in the Hubbard Model

The Mott-Hubbard metal-insulator transition is studied in the two-dimensional Hubbard Model with and without next-nearest neighbor hopping at half-filling by a combination of Quantum-Monte-Carlo and exact diagonalization techniques. In the case without next-nearest neighbor hopping, antiferromagnetic correlations are suppressed by large fluctuations due to a relatively high tempera-ture. The single particle spectral function and the spin— and charge-excitations of the metallic state below the critical Hubbard interaction U c, where the transtion occurs, are similar to the tight-binding result for U = 0. Above U c, a non-isotropic gap in the spectral function opens, and flat sidebands appear in the spectrum. The gap formation is accompanied by pronounced spin— and charge-modes. In the case including next-nearest neighbor hopping, both finite-temperature Quantum- Monte-Carlo and exact diagonalization (T = 0) results yield a metal-insulator transition at about the same critical interaction U c. However, whereas the finite- temperature transition is again of the Mott-Hubbard type, the T = 0 transition is of Mott-Heisenberg type induced by long-range antiferromagnetic correlations.