A path-integral approach to the Hubbard model is developed for the whole range of the coupling strength U. At half filling, the strong-coupling results are readily reproduced within the simple Gaussian fluctuations. The low-lying spin wave is shown to be described by the nonlinear σ model. The effective coupling of the doped hole with the background fluctuations also agrees with that obtained from the t-J model in the small-doping limit. At finite doping, such a formalism may provide a starting point for investigating the short-range spin-liquid state.

• Received 12 September 1990

DOI:https://doi.org/10.1103/PhysRevB.43.3790