The Many-Electron Problem In Novel Low-Dimensional Materials

Abstract

"Sem resumo feito pelo autor"; - This Thesis deals with the one-dimensional (1D) Hubbard model [1, 2, 3], which describes single-band interacting (correlated) electrons in a (1D) lattice. According to Lieb [4]: " The Hubbard model is to the problem of electron correlations as the Ising model is to the problem of spin-spin interactions; it is the simplest possible model displaying many "real world" features." The model depends on the parameter t, the hopping integral, characterizing the kinetic energy of the electrons when they hop between two adjacent lattice sites, and on the parameter U, the on-site Coulomb integral, characterizing the Coulomb interaction energy when two electrons occupy the same lattice site (Chapter 2). Strictly one-dimensional systems are not found in real solid-state materials, how-ever there are quasi-one-dimensional materials in nature. Theoretically, a quasi-one-dimensional. solid – the definition of which is quite broad [5]– may be represented by a three-dimensional array of one-dimensional chains, such that the hopping in-tegrais between the chains are much smaller than the hopping integral along them [6]. The correspondente with real materials – for which t and U can be estimated froco infrared spectroscopy data [7, 8, 9]– is then made by means of quantum chem-istry calculations [10], where the hopping integrais and the Coulomb on-site energy are computed by means of the atomic (molecular) wave functions of the atoms (molecules) of the solid under consideration. Obviously, approximating real materials by a simple one-dimensional model is not enough in general to make a quantitativa description of the solid properties. In spite of this, a description based on the parameters t and U contains many "real world" features [7, 8]. On the other hand, effects like electron-phonon coupling and more general Coulomb interactions, for example, are needed to account for a more quantitativa description of the physical properties of real quasi-one-dimensional materiais [11, 12, 13, 14, 15, 16, 17]. The systems described by the 1D Hubbard model (and its generalizations) have narrow energy bands, and, therefore, the tight-binding approximation for independent electrons can be applied [18].