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Journal of Physics C Solid State Physics

On the ground state phase diagram of the Hubbard model

Andrzej M. Oleś

Published Oct 30, 1982• 16 citations
Publisher

Abstract

Magnetic ordering of the Hubbard model is investigated with the help of a variational ansatz for the ground state. It is shown that only antiferromagnetic and special ferromagnetic states are stable against the paramagnetic one for the band fillings n close to n=1 and sufficiently strong Coulomb interaction.
DOI
10.1088/0022-3719/15/30/004

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We present a Hubbard model with a special hopping matrix, which has highly degenerate single-electron energy eigenstates but has different properties than the flat-band Hubbard model. Our model has a paramagnetic ground state when the electron filling factor is less than or equal to quarter-filling. In the case of quarter-filling with one extra electron, the present model exhibits saturated ferromagnetism in the ground states for a sufficiently large value of on-site Coulomb interaction but does not for a small one.
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Magnetic properties of Hubbard model have been studied extensively. A theoretical description of these states, however, is not straight forward within conventional mean-field approach due to the electron correlation effects. Here we provide a slave spin theory of the magnetic states in the single band Hubbard model. By introducing an additional decomposition of the on-site Coulomb interaction in the magnetic channel in both the slave spin and the fermionic spinon sectors, we show a magnetic solution with renormalized quasiparticle spectral weight can be stabilized at both half-filling and finite doping. By comparing the energies of antiferromagnetic and ferromagnetic states, we provide a ground-state phase diagram for generic electron filling. We further discuss possible generalization of the slave-spin method.
We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Neel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed.