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Physical review. B, Condensed matter

Antiferromagnetism in the two-dimensional infinite-UHubbard model

Z. Song, Hong Shen

Published Jun 1, 1993• 5 citations
Publisher

Abstract

The ground-state properties of the two-dimensional infinite-U Hubbard model with 1/4 hole concentration are studied with degenerate perturbation theory and an exact diagonalization method for a (2\ifmmode\times\else\texttimes\fi{}4)-site cluster. We find that on a 2\ifmmode\times\else\texttimes\fi{}4 lattice, the original model could be mapped into a spin-3/2 antiferromagnetic Heisenberg model for the case of two holes.

DOI
10.1103/physrevb.47.14576

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The ground-state properties of the two-dimensional infinite-U Hubbard model with 1/4 hole concentration are studied with degenerate perturbation theory and an exact diagonalization method for a (2\ifmmode\times\else\texttimes\fi{}4)-site cluster. We find that on a 2\ifmmode\times\else\texttimes\fi{}4 lattice, the original model could be mapped into a spin-3/2 antiferromagnetic Heisenberg model for the case of two holes.
The solution of a three-body Schr\"odinger equation (for two holes and a spin flip) shows that in the U=\ensuremath{\infty} Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.
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 two-dimensional Heisenberg model at zero temperature with a quantum S=1/2 impurity spin, coupled to one site, is studied. The ground state properties of the model are calculated for large coupling, in order to study the impurity-host spin local singlet formation and related local suppression of the magnetization in the host lattice. Analytic results are obtained by developing perturbation theory around the exactly solvable two-body (impurity plus neighbor) problem and compared with results obtained by exact diagonalization of small clusters. We find that perfect screening of the impurity is only achieved for infinitely large interaction, while at intermediate coupling the local magnetization is suppressed, but nonzero.
The infinite-U Hubbard model on finite two-dimensional square lattices is investigated by the use of exact numerical diagonalization. Configurations with one spin flip away from the ferromagnetic state and up to three holes are studied for lattice sizes ranging from 4*4 to 12*12. For all these situations, the state with one spin flip is found to be more stable than the Nagaoka ferromagnetic state. The crystal momentum of the ground state in this spin sector depends on the system size. Systematic comparison with the Gutzwiller wavefunction shows that it reproduces qualitatively the crystal momentum dependence of the energy, but not the exact correlation between the spin flip and the holes.
It is shown that for a definite cluster in the two-dimensional U=\ensuremath{\infty} Hubbard model, there are states in any Sz{\mathit{S}}^{\mathit{z}}Sz sector, which are degenerate with the lowest state in the Smaxz{\mathit{S}}_{\mathrm{max}}^{\mathit{z}}Smaxz​ sector. It is shown further that these states become the lowest ones in their sectors as the cluster becomes large enough, keeping the hole concentration constant. Then degenerate ground states of various Sz{\mathit{S}}^{\mathit{z}}Sz are obtained. The properties of the ground state of any Sz{\mathit{S}}^{\mathit{z}}SzSmaxz{\mathit{S}}_{\mathrm{max}}^{\mathit{z}}Smaxz​ can be found through those of the ground state of Smaxz{\mathit{S}}_{\mathrm{max}}^{\mathit{z}}Smaxz​.