Metal-insulator transition in the hubbard model on a triangular lattice with disorders: Renormalization group approach

A multistages block renormalization group approach to study the metal-insulator transition in the Hubbard model on a triangular lattice with hexagonal blocks is presented and implemented. A second-order phase transition with a critical point at U/t = 12.5 is obtained (the coupling parameters U and t correspond to the repulsive charging energy and to the nearest-neighbor exchange coupling terms, respectively). In the presence of disorder the phase diagram for the system exhibits a metallic phase, an insulating phase, and a domain-localized phase that separates them in the Mott regime. The subtle influence of electron-electron interactions upon inverse participation rate in the Anderson regime is also investigated. The results are discussed in light of experimental evidence for arrays of metalic quantum dots and exact numerical diagonalization of the Hubbard Hamiltonian.