Estudo do modelo de Hubbard bidimensional não homogêneo via teoria do funcional da densidade

Abstract

We implemented the DFT calculation through the Kohn-Sham formalism adapted by the methodology μ-BALDA for the inhomogeneous two-dimensional Hubbard model, which is also implemented experimentally on an ultra-cold atom traps inside of an optical lattice. This was done using the approximation LDA based on an approximation for the energy per site of the two-dimensional Hubbard model.

The main idea behind of the Kohn-Sham formalism to replace the Hubbard Hamiltonian, equivalent to a N interacting particle system, by a Hamiltonian of N non interacting particles which in our case is similar to the model of tight-binding plus an effective potential term, however both systems must have the same electronic density. This formalism leads to a self-consistent calculation, which was implement in this master degree.