Nonmagnetic Insulating States near the Mott Transitions on Lattices with Geometrical Frustration and Implications for kappa-(ET)₂Cu₂(CN)₃

We study phase diagrams of the Hubbard model on anisotropic triangular lattices, which also represents a model for $\kappa$-type BEDT-TTF compounds. In contrast with mean-field predictions, path-integral renormalization group calculations show a universal presence of nonmagnetic insulator sandwitched by antiferromagnetic insulator and paramagnetic metals. The nonmagnetic phase does not show a simple translational symmetry breakings such as flux phases, implying a genuine Mott insulator. We discuss possible relevance on the nonmagnetic insulating phase found in $\kappa$-(ET)$_2$Cu$_2(CN)_3$.