A new approach to strongly correlated fermion systems: the spin–particle–hole coherent-state path integral

Abstract

We describe a new path integral approach to strongly correlated fermion systems, considering the Hubbard model as a specific example. Our approach is based on the introduction of spin–particle–hole coherent states which generalize the spin- 1 2 coherent states by allowing the creation of a hole or an additional particle. The action of the fermion system S[γ ∗,γ; Ω] can be expressed as a function of two Grassmann variables ( γ ↑, γ ↓) describing particles propagating in the lower and upper Hubbard bands, and a unit vector field Ω whose dynamics arises from spin fluctuations. In the strong correlation limit, S[γ ∗,γ; Ω] can be truncated to quartic order in the fermionic fields and used as the starting point of a strong-coupling diagrammatic expansion in t/ U ( t being the intersite hopping amplitude and U the on-site Coulomb repulsion). We discuss possible applications of this formalism and its connection to the t- J model and the spin-fermion model.