Using the local approach, we have discussed the correlation effects of the ferromagnetic state in the Hamiltonian of a single band, and calculated the ground-state energy and the boundary condition of the phase diagram. The numerical results show that the exchange interaction j plays a decisive role for the existence of the ferromagnetic state; when Coulomb interaction u is increased, the correlation of electrons in both the paramagnetic and ferromagnetic states is increased; the larger the spin polarization m, the stronger the correlation of electrons; the Coulomb interaction w between nearest-neighbor sites depresses the correlation of electrons.
Using series expansion of local approach, the electron coupling between nearest‐neighbour sites is considered to investigate the electron correlation effect in the Hubbard model. The results show that when the off‐diagonal elements of the density matrix are considered in the calculation, it leads to an enhancement of double occupancy and are duce of the formation of the local moments.
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