[[abstract]]A new efficient converging perturbation technique valid for arbitrary interaction strength U/t and electron concentration n is applied to study strongly correlated electrons within the repulsive Hubbard model. We test the new perturbation expansion theory in terms of interacting quasi-particles about generalized self-consistent field (GSCF) solution in an entire parameter space. The developed perturbation formalism for strong interaction and large perturbation region differs from the traditional theory on the vicinity of non-interacting electrons by incorporating systematically fluctuations of quasi-particles around self-consistent solution. Performed analytical calculations of the ground state properties in the extreme conditions of one dimensionality provide quite reasonable numerical agreement with the Bethe-ansatz results in the intermediate range of U/t and n. The results are compared with the predictions of traditional perturbation theory
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