Abstract
We present a novel mean-field-like scheme for -spin fermions on a lattice in arbitrary dimension, generalizing the fermionic linearization approach. It describes the interaction of each lattice site with its neighbours by means of auxiliary fermions, living on the same site, dynamically coupled with the physical ones. This leads to a single-site picture in an enlarged 16-dimensional space given by the tensor square of the fermionic single-site Hilbert space. The general approach is applied to the extended Hubbard Hamiltonian and to the ferromagnetic Heisenberg model. The spectrum and the self-consistency equations can be determined in a straightforward way thanks to the factorization of the linearized dynamical algebra in u(n) components with n = 4 at most. The self-consistency is formulated as a fixed-point problem for a map in the space of coupling constants.
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