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Time-dependent fluctuating local field approach for description of the correlated fermions dynamics

L. D. Silakov, Ya. S. Lyakhova, A. N. Rubtsov

Abstract

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 Schrödinger 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.

Time-dependent fluctuating local field approach for description of the correlated fermions dynamics

Abstract

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 Schrödinger 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.
Paper Structure (7 sections, 8 equations, 4 figures, 1 table)

This paper contains 7 sections, 8 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Stationary FLF approach
  3. Time-dependent FLF approach
  4. Time-dependent extension of the FLF scheme
  5. Basis reduction
  6. Numerical results and discussion
  7. Conclusion

Figures (4)

  • Figure 1: Spectrum of matrix $\mathds{1}$ eigenvalues $\lambda$ divided by the maximum eigenvalue $\lambda_{max}$ and the size $n_0$ of effective basis for $2\times 2$ and $2\times 4$ half-filled Hubbard lattices.
  • Figure 2: Evolution of magnetization of $2\times 2$ half-filled Hubbard lattice embedded in $h=0.5$ magnetic field. MF approximation and TD-FLF results are compared with the numerically exact (Exact) reference data.
  • Figure 3: Evolution of magnetization of $2\times 4$ half-filled Hubbard lattice embedded in $h=0.5$ magnetic field. MF approximation and TD-FLF results are compared with the numerically exact (Exact) reference data.
  • Figure 4: Fourier spectrum of temporal magnetization oscillations of 2 $\times$ 4 Hubbard lattice. Mean-field approximation (MF) and fluctuating local field method (FLF) results are compared with the numerically exact (Exact) reference data.