We formulate a time-dependent Fluctuating Local Field (TD-FLF) method for correlated fermion dynamics, extending the stationary FLF approach. The wave function is approximated as an ensemble of noninteracting states subject to a classical fluctuating field, with dynamics encoded in the field's time-dependent distribution. This reduces the time-dependent Schrödinger equation to a generalized eigenvalue problem in a significantly reduced basis. Applied to half-filled two-dimensional Hubbard lattices, TD-FLF yields highly accurate results, outperforming mean-field theory and capturing oscillation frequencies and amplitudes in good agreement with exact diagonalization. Its low computational cost and flexibility make TD-FLF a promising tool for simulating driven correlated systems.

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• Antiferromagnetism
• Nonequilibrium statistical mechanics
• Strongly correlated systems
• Approximation methods for many-body systems
• Hubbard model
• Lattice models in condensed matter