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We establish a way to handle main collective fluctuations in correlatedquantum systems based on a Fluctuation Local Field concept. This technique goesbeyond standard mean-field approaches, such as Hartree-Fock and dynamicalmean-field theories (DMFT), as it includes a fluctuating classical field thatacts on the leading order parameter of the system. Effective model parametersof this new theory are determined from the variational principle, which allowsto resolve the Fierz ambiguity in decoupling of the local interaction term. Inthe saddle-point approximation for the fluctuating field our method reproducesthe mean-field result. The exact numerical integration over this field allowsto consider nonlinear fluctuations of the global order parameter of the systemwhile local correlations can be accounted by solving the DMFT impurity problem.We apply our method to the magnetic susceptibility of finite Hubbard systems athalf-filling and demonstrate that the introduced technique leads to a superiorimprovement of results with respect to parental mean-field approaches withoutsignificant numerical complications. We show that the Fluctuation Local Fieldmethod can be used in a very broad range of temperatures substantially belowthe N\'eel temperature of DMFT, which remains a major challenge for allexisting theoretical approaches.

Collective magnetic fluctuations in Hubbard plaquettes captured by fluctuating local field method