Abstract 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. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 360–374, 2003
The one-band two-dimensional Hubbard Hamiltonian is analyzed using a real-space renormalization-group block method. The renormalization-group method, previously applied to the one-dimensional case has been extended to two dimensions. It is also shown how to avoid the proliferation of new terms during the process if the shape of the blocks and the symmetries of the kept states are chosen conveniently. We characterize the ground state by its energy per site, the gap of charge excitations, the double occupancy, and the effective hopping. The system shows an insulating behavior in the case of half filling for all nonzero interaction parameter, U, if the hopping is isotropic (
ty=
tx); that is to say, the gap opens for all positive U, as in the one-dimensional case. If the hopping anisotropy, \ensuremath{\alpha}=
ty/
tx, is different from the unity and zero the ground state is a conductor up to a critical value (U/t
)c1, which depends on \ensuremath{\alpha}. We have analyzed in the same way another filling, n=7/9. The system behaves as a conductor, paramagnetic up to a value (U/t
)c2\ensuremath{\sim}2 and weakly ferromagnetic for higher values of U.
We have studied the Hubbard model with bond-charge interaction on a triangular lattice for a half-filled band. At the point of particle-hole symmetry the model could be analysed in detail in two opposite regimes of the parameter space. Using a real-space renormalization group (RG) we calculate the ground-state energy and the local moment over the whole parameter space. The RG results obey the exact results in the respective limits. In the intermediate region of the parameter space, the RG results clearly show the effects of the non-bipartite geometry of the lattice as well as the absence of symmetry in the reversal of the sign of the hopping matrix element.
We combine the finite-size scaling method with a multistage real-space renormalization-group procedure to examine the Mott metal-insulator transition (MIT) on a nonpartite lattice. Based on the Hubbard model, we have found that there exists a critical point
U/t=12.5 for the MIT with the correlation length exponent $\ensuremath{\nu}=1.$ At the critical point, the charge gap scales with the system size as ${▵}_{g}\ensuremath{\sim}{1/L}^{0.91}.$
We investigate the quantum phase transitions in the half-filled Hubbard model on the triangular lattice by means of the path-integral renormalization group method with a new iteration and truncation scheme proposed recently. It is found for a cluster of 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at Uc1 approximately 7.4t, which is followed by another first-order transition to a 120 degrees Néel ordered state at Uc2 approximately 9.2t, where t is the transfer integral. The size dependence of the results is also addressed. Our results suggest the existence of the intermediate NMI phase and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions.