Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0403106

Electronic states and localization in nanoscopic chains and rings from first principles: EDABI method

Gorlich, E. M., J. Kurzyk, Adam Rycerz, Roman Zahorbeński, Robert Podsiadły, W. Wójcik, Józef Spałek

Published Mar 3, 2004• 0 citations
arXivHTMLPDF

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 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.

DOI
10.48550/arxiv.cond-mat/0403106

Related papers

Electronic properties of correlated nanoscopic systems from the exact diagonalization combined with an ab initio approach

Edward M. Görlich, Adam Rycerz, Józef Spałek

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)

physica status solidi (b)•Jan 17, 2005•3 citations

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 +1 more

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.

arXiv:cond-mat/0610815•Journal of Physics Condensed Matter•May 30, 2007•20 citations

Electron correlations at nanoscale

Józef Spałek

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.

AIP conference proceedings•Jan 1, 2003•3 citations

A combined exact diagonalization - ab initio study of the metallicity and electron localization in nanoscopic systems

Adam Rycerz

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.

AIP conference proceedings•Jan 1, 2002•0 citations

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

J. Kurzyk, Józef Spałek, W. Wójcik

The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb - Wu exact solution (LW), the Gutzwiller-Wave-Function approximation (GWF), and the Gutzwiller-ansatz case (GA). The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the Exact Diagonalization combined with an Ab Initio adjustment of the single-particle wave functions in the correlated state (EDABI method). For the sake of completeness, we briefly characterize also each of the solutions. Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controllable parameter - the interatomic distance.

arXiv:0706.1266•Jun 9, 2007•0 citations

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

J. Kurzyk, Józef Spałek, W. Wójcik

The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U ) were determined for an infinite atomic chain.In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb-Wu exact solution, the Gutzwiller-wave-function approximation, and the Gutzwiller--ansatz case.The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the exact diagonalization combined with an ab initio adjustment of the single-particle wave functions in the correlated state (exact diagonalization combined with an ab initio method).For the sake of completeness, we briefly characterize also each of the solutions.Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controlable parameter -the interatomic distance.

Acta Physica Polonica A•Apr 1, 2007•9 citations
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.
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 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.
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 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.
The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb - Wu exact solution (LW), the Gutzwiller-Wave-Function approximation (GWF), and the Gutzwiller-ansatz case (GA). The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the Exact Diagonalization combined with an Ab Initio adjustment of the single-particle wave functions in the correlated state (EDABI method). For the sake of completeness, we briefly characterize also each of the solutions. Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controllable parameter - the interatomic distance.
The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U ) were determined for an infinite atomic chain.In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb-Wu exact solution, the Gutzwiller-wave-function approximation, and the Gutzwiller--ansatz case.The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the exact diagonalization combined with an ab initio adjustment of the single-particle wave functions in the correlated state (exact diagonalization combined with an ab initio method).For the sake of completeness, we briefly characterize also each of the solutions.Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controlable parameter -the interatomic distance.