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Acta Physica Sinica

Optimized structure and thermodynamic properties of atomic clusters in the framework of the extended Hubbard model

Zheng Xiao-Jun, Zhang Jun, Zhongbing Huang, 湖北大学物理学与电子技术学院,武汉 430062

Published Jan 1, 2010• 0 citations
Publisher

Abstract

By using a numerical exact diagonalization method, the properties of atomic clusters with atom number N=5 and N=6 are investigated in the framework of the extended Hubbard model. The optimized structure and the corresponding total spin S are obtained both as a function of Hubbard onsite interaction U, nearest-neighbor Coulomb repulsion V and filling number of electrons. Results show that with V increasing, the optimized structure of cluster turns into a chain or star-like structure with fewer bonds. The thermodynamic properties are also analyzed based on the distribution of energy levels of cluster with an optimized structure.

DOI
10.7498/aps.59.3897

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By using a numerical exact diagonalization method, the properties of atomic clusters with atom number N=5 and N=6 are investigated in the framework of the extended Hubbard model. The optimized structure and the corresponding total spin S are obtained both as a function of Hubbard onsite interaction U, nearest-neighbor Coulomb repulsion V and filling number of electrons. Results show that with V increasing, the optimized structure of cluster turns into a chain or star-like structure with fewer bonds. The thermodynamic properties are also analyzed based on the distribution of energy levels of cluster with an optimized structure.
The electronic, magnetic, and structural properties of small clusters are studied in the framework of the single-band Hubbard Hamiltonian. Results for various ground-state and excited-state many-body properties are presented, which were calculated exactly by means of Lanczos's numerical diagonalization method. A full geometry optimization is performed for N\ensuremath{\le}8 atoms by considering all possible nonequivalent cluster structures with fixed nearest-neighbor bond lengths. The most stable structure and the corresponding total spin S are obtained rigorously as a function of the Coulomb interaction strength U/t and number of electrons \ensuremath{\nu}. The resulting interplay between electron correlations, magnetism, and cluster structure is analyzed and the main trends as a function of N, U/t, and \ensuremath{\nu} are derived. The stability of cluster ferromagnetism is studied from two complementary points of view. First, for N\ensuremath{\le}8 and \ensuremath{\nu}=N+1, we determine exactly the stability of the ferromagnetic ground state with respect to electronic excitations and structural changes. It is shown that in small clusters the structural changes can be as important to the temperature dependence of the magnetization as the purely electronic excitations. Second, we determine the stability of the saturated ferromagnetic state with respect to single spin flips as a function of the band filling \ensuremath{\nu}/N. In this case a few selected larger clusters (7\ensuremath{\le}N\ensuremath{\le}43) in the strongly correlated limit (U/t\ensuremath{\rightarrow}+\ensuremath{\infty}) are considered. It is shown that the \ensuremath{\nu}/N dependence of the spin-flip energy \ensuremath{\Delta}${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{sf}}$ shows interesting electronic-shell-like oscillations, which reflect the characteristics of the single-particle energy-level structure and its dependence on the symmetry and size of the cluster. Finally, we conclude by discussing some of the limitations of the model together with relevant extensions. \textcopyright{} 1996 The American Physical Society.
Many-body properties of N-atom clusters having N\ensuremath{\le}8 are calculated exactly in the framework of the Hubbard model for all possible nonequivalent cluster structures. The most stable structure and the corresponding total spin S are obtained rigorously as a function of the Coulomb-interaction strength U/t and the number of electrons. Results for the stability of cluster ferromagnetism against electronic excitations and structural changes are obtained for the first time. The resulting interplay between electron correlations, magnetism, and cluster structure is determined.
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In the paper the thermodynamics of a cubic cluster with 8 sites at quarter filling is characterized by means of exact diagonalization technique. Particular emphasis is put on the behaviour of such response functions as specific heat and magnetic susceptibility. The system is modelled with extended Hubbard model which includes electron hopping between both first and second nearest neighbours as well as coulombic interactions, both on-site and between nearest-neighbour sites. The importance of hopping between second nearest neighbours and coulombic interactions between nearest neighbours for the temperature dependences of thermodynamic response functions is analysed. In particular, the predictions of Schottky model are compared with the calculations based on the full energy spectrum.
Abstract We investigate the ground state properties and the energy level statistics of a two-dimensional 3 × 3 square lattice cluster of simple and extended Hubbard model in parameters space − 10 ≤ U, V ≤ 10 for various electron configurations (N e = 10, 8, 6 and 4) within the spin subspace S = 0 using exact diagonalization. In simple Hubbard model, we observe transition from a behavior where electrons remain correlated to lattice sites to electron-paired state as U is varied from positive to negative. In case of extended Hubbard model, we observe tendency for SDW ordering (enhanced by negative V) and CDW ordering (favored by positive V), modulated by electron density. The spectral properties of energy level statistics, analyzed using kernel density estimation, reveal a complex interplay between level attraction and level repulsion, highlighting the tunability of these properties through interaction parameters.