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arXiv:cond-mat/0610815 · Journal of Physics Condensed Matter

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

Józef Spałek, Edward M. Görlich, Adam Rycerz, Roman Zahorbeński

Published May 30, 2007• 20 citations

Abstract

We overview the EDABI method developed recently and 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 localization-delocalization 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 the Fermi-Dirac-like to the Luttinger-liquid-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 to the transport properties in nanoscopic systems. For example, we show that the particle-hole symmetry is broken when the tunneling conduction through H2 molecule is calculated.

DOI: 10.1088/0953-8984/19/25/255212

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We overview the EDABI method developed recently and 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 localization-delocalization 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 the Fermi-Dirac-like to the Luttinger-liquid-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 to the transport properties in nanoscopic systems. For example, we show that the particle-hole symmetry is broken when the tunneling conduction through H2 molecule is calculated.

Abstract We provide a brief overview of the results for correlated nanoscopic systems obtained from the Exact‐Diagonalization Ab Initio (EDABI) method. Explicitly, after a brief summary of the method and its testing for the atomic and crystal‐field states, we summarize the fundamental properties of nanochains modeling a simple‐metal quantum nanowire. All the results are analyzed as a function of interatomic distance and characterize an evolution of electronic states from the Fermi‐liquid‐like state to a localized state via an intermediate Luttinger‐liquid‐like regime. The renormalized electronic (band) structure and the concept of statistical distribution function are shown to be applicable for N = 8 ÷ 16 atoms arranged in chain or ring configurations. The role of boundary conditions involving a ficticious flux representing the Berry phase is also briefly discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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 single-particle 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.

We present our new method of approach to the interacting electron systems combining the exact diagonalization of the Hamiltonian in the Fock space (including all hopping integrals and all two‐site interactions) with an ab initio optimization of the single particle (Wannier) functions in the resultant ground state. Such a procedure is applied to the analysis of the electron localization in nanoscopic chains containing up to N = 12 atoms. Electrons are essentially localized for the interatomic distance R > 2.2 Å. The statistical distribution evolves from the Fermi‐liquid limit (at R ∼ 1 − 2 Å) to continuous momentum distribution for R > 2.2 Å. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. Futher applications of our method are listed at the end.

We briefly summarize the fundamental properties of correlated nanoscopic systems obtained within the EDABI method combining an exact diagonalization in the Fock space with an ab initio readjustment of the single‐particle wave functions in the resultant ground state. Explicitly, we address the following questions: evolution of various systems from a nanometal to a nanoinsulator of the Mott‐Hubbard type, the appearance of the Mott‐Hubbard gap in molecular and cluster (Hn) systems, as well as the stability of those clusters.

We review our recent results concerning the electronic properties of a nanoscopic system with inclusion of long‐range Coulomb interactions that are obtained by combining exact diagonalization in the Fock space with an ab initio method (EDABI). The system evolution is discussed as a function of lattice parameter R. A transformation from a nanometal to localized spin system is observed. With the help of a finite‐size scaling we determine the discontinuity of the momentum distribution at the Fermi points. Our results imply Fermi‐liquid‐like behavior for R ≲ 3a0 (a0 is the Bohr radius). The quasiparticle mass is almost divergent at the localization threshold, where the particle distribution of the Fermi‐Dirac type gets smeared out. The charge‐gap evolution is compared with that of the Slater gap. Also, the single‐particle spectral function and the corresponding density of states are presented. The analysis is performed using 1s‐like Gaussian‐type STO‐3G basis.