Interaction quenches in the two-dimensional fermionic Hubbard model

The generic nonequilibrium evolution of a strongly interacting fermionic system is studied. For strong quenches, a collective collapse-and-revival phenomenon is found to extend over the whole Brillouin zone. A qualitatively distinct behavior occurs for weak quenches where only weak wiggling occurs. Surprisingly, no evidence for prethermalization is found in the weak-coupling regime. In both regimes, indications for relaxation beyond oscillatory or power-law behavior are found and used to estimate relaxation rates without resorting to a probabilistic ansatz. The relaxation appears to be fastest for intermediate values of the quenched interaction.

Figure 1

Evolution of the momentum distribution of the half-filled Hubbard model quenched to $U=2W$. Only one quadrant of the Brillouin zone is shown due to point-group symmetry. The data result from $n=6$ commutations.

Figure 2

Jump $\Delta n\left(t\right)$ calculated at two positions on the Fermi surface for various interaction strengths $U$. The curves for $U=1.0W$ change their style for larger times; at that point we no longer consider them fully reliable.

Figure 3

Comparison of the time dependence of the jump $\Delta n\left(t\right)$ for various $U$ in half-filled Hubbard models: Solid lines show the 2D, and the dashed lines of the corresponding grayscale (color) show the 1D data.

Figure 4

Fits (dashed lines) to the jump $\Delta n\left(t\right)$ from the EOM (solid lines) for quenches to strong interactions; fits based on Eq. (3).

Figure 5

Fit parameters as they result from fitting the EOM data by Eq. (3) for strong interactions and by (7) for weak interactions. The dashed lines for $U/(U_C/2+U)⪆0.86$ depict fits which are unstable and cannot be done without restrictions in the range of parameters. The left scale applies to $a$ and $b$ while the right one to $T$. In the transition region between the two dashed perpendicular lines our data does not allow us to decide on the nature of the quench, weak or strong. The constant $U_C$ is set to $-8E_{\mathrm{kin}}=(16/{\pi }^2)W=1.62W$.

Figure 6

Leading perturbative correction $f_{k_F}\left(t\right)$ as it appears in (4) and is defined in (5) evaluated in 2D for the half-filled Hubbard model at two different momenta on the Fermi surface. Logarithmic fits are included.

Figure 7

Fits (dashed lines) to the jump $\Delta n\left(t\right)$ from the EOM (solid lines) for quenches to weak interactions, fits based on Eq. (7). Exemplarily for $U=0.5W$, the dotted line shows $\Delta n_{k_F,2\mathrm{nd}}\left(t\right)$ from Eq. (4) and the dashed-dotted line $\Delta n_{k_F,\exp }\left(t\right)$ from Eq. (6).