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Journal of Physics C Solid State Physics

Ground-state properties of strongly correlated electrons on finite clusters

Antonis D Mistriotis, H. Büttner, W. Pesch

Published Oct 30, 1988• 4 citations
Publisher

Abstract

The authors have analysed finite clusters with different degrees of frustration on the basis of the conventional Hubbard model. In particular they have calculated the ground-state energy and certain correlation functions as a function of the interaction energy U. As U varies, a sharp transition is observed between two different structures for half-filled bands. The authors have studied these clusters not only for the case of a half-filled band but also for different numbers of holes. They found that the structure of the ground state depends critically on the total spin and the number of holes.

DOI
10.1088/0022-3719/21/30/004

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The authors have analysed finite clusters with different degrees of frustration on the basis of the conventional Hubbard model. In particular they have calculated the ground-state energy and certain correlation functions as a function of the interaction energy U. As U varies, a sharp transition is observed between two different structures for half-filled bands. The authors have studied these clusters not only for the case of a half-filled band but also for different numbers of holes. They found that the structure of the ground state depends critically on the total spin and the number of holes.
We analyze the ground-state properties of the U=\ensuremath{\infty} Hubbard model on a 4\ifmmode\times\else\texttimes\fi{}4 cluster using a Lanczos technique. The quantum numbers of the ground-state, its momentum distribution, the magnetic structure factor, some 〈nˆk{\mathrm{\^{}}}_{\mathbf{k}}ˆk​n${\mathrm{\^{}}}_{\mathbf{k}\ensuremath{'}}$〉 dynamic correlation functions, and the overlap of the ground state with the noninteracting one (both before and after a Gutzwiller projection) are given for all fillings. As the number of electrons approaches half-filling the system undergoes a transition from a conventional ground state that overlaps appreciably with the noninteracting one to a new ground state that shows local ferromagnetic correlations and negligible overlap with the corresponding U=0 ground state. A detailed analysis of the wave function corresponding to the ground state of 14 electrons (two holes) proves the existence of a finite shift of the Fermi surface. Our results support the existence of a stable magnetic phase at small but finite hole doping. This new magnetic phase is locally ferromagnetic although the total spin is not maximum.
The ground-state wave function and energy are calculated for the one-band Hubbard Hamiltonian on a 4\ifmmode\times\else\texttimes\fi{}4 cluster of the square lattice up to first and second order of the on-site Coulomb repulsion U, respectively. Changes induced by a deviation of the number of electrons from half-filling (one electron per lattice site) are closely followed. Charge-charge and spin-spin correlation functions are directly obtained from the ground-state wave function and show the existence of antiferromagnetic correlations that extend over the whole cluster at half-filling. Correlations among sites separated by more than a lattice site diminish very rapidly as holes are introduced into the cluster. The analysis is extended to the negative-U case. Ground-state properties change qualitatively.
The single-band Hubbard model (both with and without first-neighbor interactions) is studied by exact diagonalization on several one- and two-dimensional clusters, ranging from four to nine sites, including rings and arrangements of squares. Occupancies include the half-filled band (one electron per site) and configurations with one and two holes in the half-filled band. Ground-state properties are determined for a wide range of parameters. We discuss the phase diagram in the (U,V) plane and consider spin, charge, and pairing correlations. The binding of a pair of holes is investigated. Circumstances in which binding and pairing are enhanced by first-neighbor interactions are described.
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.
With the aim of contributing to a better understanding of the finite-temperature properties of low-dimensional strongly correlated systems we study a one-dimensional half-filled-band extended Hubbard model with a term of exchange interaction between neighboring sites. We analyze the temperature dependence of the specific heat, internal energy, entropy, number of doubly occupied sites, magnetic susceptibility, spin-spin correlation functions, and also investigate a detailed diagram of magnetic correlations. We use the method of small-cluster exact diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined model exhibits a rich structure of magnetic properties due to the competition between the onsite Coulombian repulsion and the exchange interaction.