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Systems with strong electronic Coulomb correlations often display rich phasediagrams exhibiting different ordered phases involving spin, charge, or orbitaldegrees of freedom. The theoretical description of the interplay of thecorresponding collective fluctuations giving rise to this phenomenology remainshowever a tremendous challenge. Here, we introduce a multi-channel extension ofthe recently developed fluctuating field approach to competing collectivefluctuations in correlated electron systems. The method is based on avariational optimization of a trial action that explicitly contains the orderparameters of the leading fluctuation channels. It gives direct access to thefree energy of the system, facilitating the distinction between stable andmeta-stable phases of the system. We apply our approach to the extended Hubbardmodel in the weak to intermediate coupling regime where we find it to capturethe interplay of competing charge density wave and antiferromagneticfluctuations with qualitative agreement with more computationally expensivemethods. The multi-channel fluctuation field approach thus offers a promisingnew route for a numerically cheap treatment of the interplay between collectivefluctuations in large systems.

Multi-channel fluctuating field approach to competing instabilities in interacting electronic systems