Abstract
The entire energy spectrum is calculated numerically for the two-dimensional Hubbard model on square lattices with four electrons varying the interaction strength U in a wide range. Taking all symmetries explicitly into account a level statistical analysis is performed on this strongly correlated 2D system. The level spacing distribution and the number variance exhibit a random matrix (GOE) behavior for all positive values of U, the latter however only up to a medium energy scale λ* ≈ 3 independent of U.