Electronic States of Nanoscopic Chains and Rings from First Principles: EDABI Method

Abstract

We summarize briefly the main results obtained within the proposed EDABI method combining Exact Diagonalization of (parametrized) many-particle Hamiltonian with Ab Initio self-adjustment of the singleparticle wave function in the correlated state of interacting electrons. The properties of nanoscopic chains and rings are discussed as a function of their interatomic distance R and compared with those obtained by Bethe ansatz for infinite Hubbard chain. The concepts of renormalized orbitals, distribution function in momentum space, and of Hubbard splitting as applied to nanoscopic systems are emphasized.

Lieb-Wu Solution, Gutzwiller-Wave-Function, and Gutzwiller-Ansatz Approximations with Adjustable Single-Particle Wave Function for the Hubbard Chain

“…ten Coulomb wells from the left and 11 potential wells from the right. We have also made (for comparison) the calculations for k = 2 and have compared the results with the previous calculations for nanochains [12,13]. Our results show that taking 6 Coulomb potential wells is indeed sufficient.…”

“…In that approximation, the whole approach reduces to the combinatorial problem of calculating the number of configurations. In this work we present the combined of single-particle wave function in the correlated state [2,3,11,12] with the exact [5] or approximate ‡ [6,10,13] of the correlations. The original Gutzwiller approach is regarded sometimes as cumbersome.…”

“…Hence, to make the problem tractable, we approximate the wave functions as the combinations of seven Gaussians (STO-7G basis) and compared them with those for STO-3G basis (combination of the three Gaussians) [12,13]. The used STO-7G basis did not lead to a qualitative improvement of results when compared to those with STO-3G basis.…”

Correlated Electron Systems of Different Dimensionalities

“…We extended the method (exact diagonalization combined with the ab initio approach, EDABI) used earlier for analysis of correlated nanoscopic systems [1][2][3][4][5] to infinite (periodic) s-band-like systems described by the Hubbard model and its extensions. We describe correlated electron systems of different dimensionalities and symmetries by using the extended Hubbard Hamiltonian…”