Regular Perturbation Theory About Generalized Self-Consistent Field Hamiltonian

Strongly correlated electrons require non-traditional approaches to describe their unexpected properties. The perturbation theory about non-interacting electron gas first developed by Abrikosov and Khalatnikov has a zero convergence radius for the resulting perturbation series. The analytical theory of Gell-Mann and Bruckner, now known as random phase approximation (RPA), gives exact values for the correlation energy in the high density-weak coupling regime. However, this method also runs into difficulties due to the insufficient treatment of fluctuations. We give a formulation of a regular perturbation theory within the repulsive Hubbard model for interacting quasi-particles about exactly solvable generalized self-consistent field (GSCF) Hamiltonian for studying the intermediate range of interaction strength $U/t$, where there is no small parameter. Proposed perturbation series for interacting quasi-particles in entire parameter space of $U/t$ and electron concentration $n$ do not diverge. Performed analytical calculations of the ground state properties in extreme conditions of one dimensionality provide good numerical agreement with the Bethe-{\it ansatz} results and reasonable interpolation scheme for intermediate range of $U/t$ and $n$. The method can be used also for studies electron correlations in finite size clusters.