Metal-insulator transition accompanied with a charge ordering in the one-dimensional model

We study the metal-insulator transition accompanied with a charge ordering in the one-dimensional (Formula presented)-(Formula presented) model at quarter filling by the density-matrix renormalization-group method. In this model the nearest-neighbor hopping energy (Formula presented) competes with the next-nearest-neighbor exchange energy (Formula presented). We have found that a metal-insulator transition occurs at a finite value of (Formula presented); (Formula presented) and the transition is of first order. In the insulating phase for small (Formula presented), there is an alternating charge ordering and the system behaves as a one-dimensional quantum Heisenberg antiferromagnet. The metallic side belongs to the universality class of the Tomonaga-Luttinger liquids. The quantum phase transition is an example of melting of the one-dimensional quantum Heisenberg antiferromagnet.