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

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We study phase diagrams of the Hubbard model on anisotropic triangular lattices, which also represents a model for κ-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 κ-(ET)₂Cu₂(CN)₃.