Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice

The half-filled Hubbard model on the Bethe lattice with coordination number z=3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization , its fluctuations and various spin correlation functions are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors []. At large U/t, is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ for ]. shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of with increasing U/t and the formation of important permanent moments at large U/t. While NN sites show antiferromagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U=0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates. Received 8 February 1999 and Received in final form 14 June 1999     

Influence of synthesis conditions over simonkolleite/ZnO precipitation

Simonkolleite is a zinc-layered hydroxide salt with the formula Zn₅(OH)₈Cl₂·H₂O. It has a platelet morphology and can be used for many applications, owing to both its layered structure and its nature as a hydroxide salt. It can be prepared via a simple precipitation from ZnCl₂ and NaOH in water thermostated at 50 °C. Depending on the synthesis conditions, we could obtain different sizes and a hybrid containing parts of ZnO. We studied the influence of the OH:Zn molar ratio, the addition order, and the maturation time after the reaction was completed. With the support of pH profiles, kinetic studies, and thermodynamic equilibrium data, we were able to propose a global synthesis mechanism explaining the influence of those three parameters and identify the range of conditions in which simonkolleite can be formed. Depending on the desired application, we were able to synthesize bigger or smaller layered crystals of simonkolleite, in the presence of absence of ZnO.     

Coupled cluster treatments of periodic systems from strongly localized reference functions: 1-D and 2-D spin and electron lattices

A modified coupled cluster method is applied to the research of the ground-state energy of periodic systems described by model Hamiltonians. The reference function is always a strongly localized function. The method is applied first to Heisenberg Hamiltonians and spin-frustrated one-dimensional (1-D) chain and square lattices, starting from Neel functions or from products of bond singlets. The same method is then applied to Hubbard Hamiltonian for 1-D chain and two-dimensional (2-D) square lattices starting from Neel function or products of bond molecular orbitals (MOs). In both cases the wave operators involve a very limited number of local operators. Despite its simplicity, the method is able to treat quite satisfactorily highly degenerate situations, approaching correctly the highly delocalized regime from the Neel function or the highly correlated regime from a product of bond MOs. However, the method is not precise enough to treat the subtle phenomenon of bond alternation of polyacetylene. The coupled cluster method from strongly localized reference functions represents an elegant and quite efficient exploratory tool, but its accuracy is limited by the poor treatment of collective effects. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 115–132, 1998