We formulate a time-dependent Fluctuating Local Field (TD-FLF) method for correlated fermion dynamics, extending the stationary FLF approach. The wavefunction is approximated as an ensemble of non-interacting states subject to a classical fluctuating field, with dynamics encoded in the field's time-dependent distribution. This reduces the time-dependent Schr\"odinger equation to a generalized eigenvalue problem in a significantly reduced basis. Applied to half-filled 2D 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.
@article{arxiv.2512.21772,
title = {Time-dependent fluctuating local field approach for description of the correlated fermions dynamics},
author = {L. D. Silakov and Ya. S. Lyakhova and A. N. Rubtsov},
journal= {arXiv preprint arXiv:2512.21772},
year = {2026}
}