| Summary: | 碩士 === 淡江大學 === 物理學系碩士班 === 93 === In this thesis a new perturbation method is developed to calculate corrections to generalized self-consistent field (GSCF) approximation of the Hubbard model solution. This perturbation method regards the GSCF solution as the zero order approximation and is able to get converging results in a more wide parameter range than the tranditional perturbation method. The tranditional perturbation method regards the system of the non-interacting electrons as the zero order approximation and is suitable only for the weak interaction intensities (|U|/t<<1).
In this thesis the one- and two-dimentional repulsive Hubbard model is analysed in detail . The calculated gound state properties, namely, the energy, the double occupancy andthe kinetic energy are compared with Bethe-ansatz exact results in the one-dimensional case. Investigation is carried out for the general electronic density value, general interaction intensity value, and general magnetic field value. In certain n, U, h ranges, the perturbation and exact results are quite close and they coincide at weak and strong coupling limits.
This thesis for the first time presents the two-dimentional GSCF results. In
addition of the above mentioned ground state physical quantities, the chemical
potential, transverse and longitudinal spin, and the wave verctor of transverse spin are
discussed as well. In the two-dimentional system a paramagnetic state and some one
order phase transitions appear in specific cases. This phenomenon does not exist in the
one-dimensional case.
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