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Journal of Physics Condensed Matter

Holes in finite electron systems with strong correlation

Antonis D Mistriotis, H. Büttner, W. Pesch

Published Feb 6, 1989• 4 citations
Publisher

Abstract

The ground-state properties of several finite two-dimensional clusters were numerically investigated within the Hubbard model. In particular the spatial distribution of holes (with respect to the half-filled band case) is studied in detail. It is found that in systems with frustrated sites the holes prefer to occupy these sites for large U, and repel each other. This effect can be used to stabilise the antiferromagnetic order in the clusters by introducing coupling to additional sites.

DOI
10.1088/0953-8984/1/5/005

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The ground-state properties of several finite two-dimensional clusters were numerically investigated within the Hubbard model. In particular the spatial distribution of holes (with respect to the half-filled band case) is studied in detail. It is found that in systems with frustrated sites the holes prefer to occupy these sites for large U, and repel each other. This effect can be used to stabilise the antiferromagnetic order in the clusters by introducing coupling to additional sites.
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 investigate the Hubbard model on a two-dimensional cluster of 18 sites using Lanczos algorithm for different strengths of Coulomb repulsion in the low doping region. Energies and correlation functions are given for half-filling and two holes. In the strong coupling regime we compare our results with the $t\ensuremath{-}J$ model. We confirm the tendency of holes to repel, although a significant value of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductive order parameter is measured. These data represent a benchmark for future quantum simulations.
The effective Hamiltonian, obtained from the Hubbard model in the strong-coupling limit, is diagonalized exactly for a periodic two-dimensional square lattice of ten sites. We obtain the ground state of the system for any filling of the lattice and the KKK-space excitation spectrum for a single hole. Within our finite-size system, it is found that for very small coupling ratio tU\frac{t}{U}Ut​, each hole creates a local ferromagnetic environment at least of the size of our system, whereas for increasing tU\frac{t}{U}Ut​, the holes tend to form clusters, induced by antiferromagnetic spin correlations. A range of tU\frac{t}{U}Ut​ exists for which pairing of the holes may be possible.
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.