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Physical review. B, Condensed matter

Ground-state and thermodynamic properties of the Hubbard model applied to small clusters

J. Callaway, D. P. Chen, R. Tang

Published Mar 15, 1987• 61 citations
Publisher

Abstract

The Hubbard Model with nearest-neighbor hopping and one type of orbital is applied to small clusters, with emphasis on an octahedron (six sites). The complete eigenvalue spectrum is calculated. A rather complicated dependence of the spin of the ground state on occupation number, geometry, and model parameters is found. Thermodynamic properties are computed with use of a canonical ensemble. Results are reported for the specific heat, spin susceptibility, and spin-spin correlation functions.

DOI
10.1103/physrevb.35.3705

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The Hubbard Model with nearest-neighbor hopping and one type of orbital is applied to small clusters, with emphasis on an octahedron (six sites). The complete eigenvalue spectrum is calculated. A rather complicated dependence of the spin of the ground state on occupation number, geometry, and model parameters is found. Thermodynamic properties are computed with use of a canonical ensemble. Results are reported for the specific heat, spin susceptibility, and spin-spin correlation functions.
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The eigenvalue problem of the two-site and three-site extended Hubbard Hamiltonian, which contains the intraatomic repulsion UUU, the nearest-neighbor repulsion VVV, the isotropic exchange JJJ, the anisotropic exchange ${J}^{\ensuremath{'}}$, the hopping term ttt, the semihopping term SSS, and the double hopping term DDD, has been solved exactly and the grand partition function is obtained. The magnetic and thermodynamic quantities such as the magnetic susceptibility and the specific heat are calculated for arbitrary electron density. Several features believed to have wider validity have been deduced from this cluster model.
We study the thermodynamics of a zero-dimensional, cubic cluster described with a Hubbard Hamiltonian, focusing our interest on the magnetic properties. The range in which the studied cluster is paramagnetic is considered. The results are obtained by means of exact numerical diagonalization. Such thermodynamic quantities as entropy, specific heat, magnetic susceptibility, spin-spin correlations and double occupancy are discussed. Particular emphasis is put on the behaviour of local maxima of specific heat and susceptibility, which are analysed in terms of Schottky anomalies.
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.
All the energy eigenvalues of the Hubbard model with infinite repulsion on 2×2×2 cubic lattice for different electron numbers N e are calculated numerically. For N e =4, 7 the ground state is completely ferromagnetic; namely, total spin S is N e /2. For N e =5, the total spin of the ground state is 3/2. For N e =2, 6, it is zero. For N e =1, 3, it is 1/2. Thermodynamic quantities such as entropy, susceptibility and specific heat are calculated with the method of canonical ensemble. There are two peaks in the specific heat curve for N e =4, 5, 6, 7, but only one peak for N e =1, 2, 3.
Abstract The Hubbard model on a cube was revisited and extended by both nearest‐neighbor Coulomb correlation W and nearest‐neighbor Heisenberg exchange J. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on‐site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossings depending on the various model parameters. Furthermore the groundstates of the pure Hubbard model in dependence on a magnetic field h coupled to the spins are shown for the complete U‐h plane. The critical magnetic field, where the zero spin groundstate breaks down is given for four and six electrons. Suprisingly we found parameter regions, where the ground state spin does not depend monotonously on J in the extended model. For the cubic cluster gas, i.e. an ensemble of clusters coupled to an electron bath, we calculated the density n (μ, T, h) and the thermodynamical density of states from the grand potential. The ground states and the various spin‐spin correlation functions are studied for both attractive and repulsive values of the three interaction constants. We determined the various anomalous degeneration lines, where n (μ, T = 0, h = 0) shows steps higher than one, since in this parameter regions exotic phenomena as phase separation are to expect in extended models. For the cases where these lines end in triple points, i.e. groundstates of three different occupation numbers are degenerated, we give the related parameter values. Regarding the influence of the nn‐exchange and the nn‐Coulomb correlation onto the anomalous degeneration we find both lifting and inducing of degeneracies depending on the parameter values.