The combined exact diagonalization–ab initioapproach and its application to correlated electronic states and Mott–Hubbard localization in nanoscopic systems

Abstract

We overview the EDABI method developed recently combining the exact diagonalization and ab initio aspects of electron states in correlated systems and apply it to nanoscopic systems. In particular, we discuss the localizationdelocalization transition for the electrons that corresponds to the Mott-Hubbard transition in bulk systems. We show that the statistical distribution function for electrons in a nanochain evolves from Fermi-Dirac-like to Luttingerliquid-like with the increasing interatomic distance. The concept of Hubbard subbands is introduced to nanoclusters, and corresponds to the HOMO-LUMO splitting in the molecular and organic solid states. Also, the nanochains exhibit magnetic splitting (Slater-like), even without the symmetry breaking, since the spin-spin correlations extend over the whole system. Thus, the correlated nanoscopic systems exhibit unique and universal features, which differ from those of molecular and infinite systems. These features define unique properties reflecting 'the Mott physics' on the nanoscale. We also employ the EDABI method for the transport properties in nanoscopic systems. For example, we show that the particle-hole symmetry is broken when the tunnelling conduction through the H 2 molecule is calculated.

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

“…Therefore, the single-particle wave function of the Wannier type are adjusted a posteriori, in the correlated state, as the electron correlations and the single-particle aspect of the problem are treated on the same footing. This method is suited particularly for correlated nanoscopic systems [3,12]. In general, it is suited (as it is the case here) for the situations when the interaction is of nonperturbative nature and the expression for the ground-state energy obtained in either analytic form or iteratively.…”

“…We can rewrite the intersite part of the electron-electron interaction in the form 3) where N e is the total number of electrons in the system, N a is the number of atoms (ions), and δn i = n i − 1. In the considered here Mott insulating state we have on average δn i = 0, achieved for N e = N a (the narrow band is half-filled, n = 1) and therefore…”

“…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.…”

“…As a result, we obtain the renormalized (self-adjusted) wave equation (SWE) for those wave functions, which include explicitly the effect of correlations. This method combines in a natural manner the 2nd and 1st quantization schemes and, in principle, the only approximation made is the limitation of the basis size, which is explicitly contained in the definition of the model considered [3].…”

“…We applied it to the nanoscopic systems and have addressed the question concerning the "Mott physics" as applied to a nanoscopic scale [3,4]. Here we apply the same scheme to the one-dimensional Hubbard model, for which the exact solution of Lieb-Wu (LW) [5] is available.…”