  Systems with strong electronic Coulomb correlations often display rich phase
diagrams exhibiting different ordered phases involving spin, charge, or orbital
degrees of freedom. The theoretical description of the interplay of the
corresponding collective fluctuations giving rise to this phenomenology remains
however a tremendous challenge. Here, we introduce a multi-channel extension of
the recently developed fluctuating field approach to competing collective
fluctuations in correlated electron systems. The method is based on a
variational optimization of a trial action that explicitly contains the order
parameters of the leading fluctuation channels. It gives direct access to the
free energy of the system, facilitating the distinction between stable and
meta-stable phases of the system. We apply our approach to the extended Hubbard
model in the weak to intermediate coupling regime where we find it to capture
the interplay of competing charge density wave and antiferromagnetic
fluctuations with qualitative agreement with more computationally expensive
methods. The multi-channel fluctuation field approach thus offers a promising
new route for a numerically cheap treatment of the interplay between collective
fluctuations in large systems.
