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 $S[{\gamma }^{\ast },\gamma ;\mathbf{\Omega }]$ can be expressed as a function of two Grassmann variables (${\gamma }_{\uparrow }$,${\gamma }_{\downarrow }$) describing particles propagating in the lower and upper Hubbard bands, and a unit vector field $\mathbf{\Omega }$ whose dynamics arises from spin fluctuations. In the strong correlation limit, $S[{\gamma }^{\ast },\gamma ;\mathbf{\Omega }]$ 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.

20 pages RevTex, 10 figures

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