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Physics Letters A

Ground state of the half-filled extended Hubbard model beyond the Hartree-Fock approximation

Andrzej M. Oleś, R. Micnas, S. Robaszkiewicz, K. A. Chao

Published May 1, 1984• 13 citations
Publisher
DOI
10.1016/0375-9601(84)90692-3

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Progress of Theoretical Physics•May 1, 1975•45 citations
We revisit the unrestricted Hartree Fock study on the evolution of the ground state of the Hubbard model on the triangular lattice with hole doping. At half-filling, it is known that the ground state of the Hubbard model on triangular lattice develops a 120 degree coplanar order at half-filling in the strong interaction limit, i.e., in the spin 1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. The ground state property in the doped case is still in controversy even though extensive studies were performed in the past. Within Hartree Fock theory, we find that the 120 degree order persists from zero doping to about 0.3 hole doping. At 1/3 hole doping, a three-sublattice collinear order emerges in which the doped hole is concentrated on one of the three sublattices with antiferromagnetic Neel order on the remaining two sublattices, which forms a honeycomb lattice. Between the 120 degree order and 1/3 doping region, a phase separation occurs in which the 120 degree order coexists with the collinear anti-ferromagnetic order in different regions of the system. The collinear phase extends from 1/3 doping to about 0.41 doping, beyond which the ground state is paramagnetic with uniform electron density. The phase diagram from Hartree Fock could provide guidance for the future study of the doped Hubbard model on triangular lattice with more sophisticated many-body approaches.
The method of Gutzwiller in the problem of electron correlation in the Hubbard model is extended to the antiferromagnetic state. It is shown that the transition from the paramagnetic to the antiferromagnetic state occurs at a certain value of U (intraatomic Coulomb energy) for a fixed value of the electron concentration. In contrast to the result in the Hartree-Fock approximation, this value of U does not vanish even in the case when the magnetic zone boundary coincides with the Fermi surface. For extremely large values of U, the critical electron concentration is shown to approach to 1/2. Special care is taken in the case of the half-filled band, and our ground state energy is compared with that in the Hartree-Fock approximation. It is shown that for large value of U the Hartree-Fock energy is lower, but that for intermediate value of U our energy becomes lower for the special band structure.