Magnetic properties and Mott transition of the Hubbard model for weakly coupled chains on the anisotropic triangular lattice

We investigate the magnetic properties and Mott transition in the Hubbard model for weakly coupled chains on the anisotropic triangular lattice. Taking into account 120$^\circ$ N\'eel, and collinear orderings, the magnetic phase diagram is studied at zero temperature and half-filling by the variational cluster approximation. We found that when the on-site Coulomb repulsion $U$ is relatively large, nonmagnetic insulator, which is a candidate of the spin liquid state, is realized for wide range of the interchain hopping from quasi two-dimensional to almost one-dimensional regime. When the interchain hopping is relatively large, this nonmagnetic insulator becomes magnetic states as $U$ decreases. For rather small interchain hopping, it changes to the paramagnetic metal, thus purely paramagnetic metal-insulator transition (Mott transition) takes place. Implications of our results for the Cs$_2$CuBr$_4$ and Cs$_2$CuCl$_4$ are discussed.