Fundamental properties, localization threshold, and the Tomonaga--Luttinger behavior of electrons in nanochains

We provide a fairly complete discussion of electronic properties of nanochains modelling the simplest quantum nanowires, within the recently proposed approach combining Exact Diagonalization in the Fock space with an Ab Initio calculations (EDABI method). In particular, the microscopic parameters of the second-quantized Hamiltonian are determined and the evolution of the system properties is traced in a systematic manner as a function of the interatomic distance (the lattice parameter, R). Both the many-particle ground state and the dynamical correlation functions are discussed within a single scheme. The principal physical results are: (i) the evolution of the electron momentum distribution and its analysis in terms of the Tomonaga-Luttinger scaling, (ii) the appearance of mixed metallic and insulating features partial localization) for the half-filled band case, (iii) the appearence of a universal renormalized dispersion relation of electron energy, which incorporates both the band-structure and the Hubbard-splitting features in the presence of electron interactions, and (iv) the transformation from a highly-conducting nanometalic state to the charge-ordered nanoinsulator in the quarter-filled case. The analysis is performed using an adjustable Gaussian 1s-like basis set composing the Wannier functions, as well as includes the long-range Coulomb interaction.