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

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[gamma*, gamma; Omega] can be expressed as a function of two Grassmann variables (gamma (up arrow),gamma (down arrow)) describing particles propagating in the lower and upper Hubbard bands, and a unit vector field Omega whose dynamics arises from spin fluctuations. In the strong correlation limit, S[gamma*, gamma; Omega] 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. (C) 2001 Elsevier Science B.V. All rights reserved.