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Physical review. B, Condensed matter

Enhancement of binding energies in linked Hubbard clusters

Richard M. Fye, Douglas J. Scalapino, Richard T. Scalettar

Published Oct 1, 1992• 10 citations
Publisher

Abstract

We calculate the binding energy of a pair of holes doped into half-filled Hubbard clusters which are linked together. For some geometries, two linked clusters exhibit binding which is monotonically reduced by intercluster hopping, as is the case between simple negative-U centers. However, for certain of the geometries, we find that binding in the linked clusters can be considerably enhanced over that of the individual clusters, or, in some cases, even induced by a relatively weak linking. In these cases, the new binding is not simply a stabilization of that for individual clusters, but instead reflects a partial sharing of the hole pair between clusters.

DOI
10.1103/physrevb.46.8667

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We calculate the binding energy of a pair of holes doped into half-filled Hubbard clusters which are linked together. For some geometries, two linked clusters exhibit binding which is monotonically reduced by intercluster hopping, as is the case between simple negative-U centers. However, for certain of the geometries, we find that binding in the linked clusters can be considerably enhanced over that of the individual clusters, or, in some cases, even induced by a relatively weak linking. In these cases, the new binding is not simply a stabilization of that for individual clusters, but instead reflects a partial sharing of the hole pair between clusters.
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.
I present a scheme for performing weak-coupling expansions for the Hubbard model on square clusters near half-filling. Using this scheme the 6 × 6 cluster with 2, 3 and 4 holes is considered. I have calculated the ground-state quantum numbers for the 3- and 4-hole cases. In the 3-hole case I find a nonzero momentum near the (±π/2, ±π/2) points, while for the four-hole case the momentum is (0, 0). The calculation of low-lying excited states indicates the opening of a spin gap as one dopes away from half-filling.
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.