  One-dimensional systems have unusual properties such as fractionalization of
degrees of freedom. Possible extensions to higher dimensional systems have been
considered in the literature. In this work we construct a mean field theory of
the Hubbard model taking into account a separation of the degrees of freedom
inspired by the one-dimensional case and study the finite-temperature phase
diagram for the Hubbard chain and square lattice. The mean field variables are
defined along the links of the underlying lattice. We obtain the spectral
function and identify the regions of higher spectral weight with the
fractionalized fermionic (spin) and bosonic (charge) excitations.
