  We establish a way to handle main collective fluctuations in correlated
quantum systems based on a Fluctuation Local Field concept. This technique goes
beyond standard mean-field approaches, such as Hartree-Fock and dynamical
mean-field theories (DMFT), as it includes a fluctuating classical field that
acts on the leading order parameter of the system. Effective model parameters
of this new theory are determined from the variational principle, which allows
to resolve the Fierz ambiguity in decoupling of the local interaction term. In
the saddle-point approximation for the fluctuating field our method reproduces
the mean-field result. The exact numerical integration over this field allows
to consider nonlinear fluctuations of the global order parameter of the system
while local correlations can be accounted by solving the DMFT impurity problem.
We apply our method to the magnetic susceptibility of finite Hubbard systems at
half-filling and demonstrate that the introduced technique leads to a superior
improvement of results with respect to parental mean-field approaches without
significant numerical complications. We show that the Fluctuation Local Field
method can be used in a very broad range of temperatures substantially below
the N\'eel temperature of DMFT, which remains a major challenge for all
existing theoretical approaches.
