Nonthermal Steady States after an Interaction Quench in the Falicov-Kimball Model

We present the exact solution of the Falicov-Kimball model after a sudden change of its interaction parameter using nonequilibrium dynamical mean-field theory. For different interaction quenches between the homogeneous metallic and insulating phases the system relaxes to a nonthermal steady state on time scales on the order of $\hslash /\mathrm{\text{bandwidth}}$, showing collapse and revival with an approximate period of $h/\mathrm{\text{interaction}}$ if the interaction is large. We discuss the reasons for this behavior and provide a statistical description of the final steady state by means of generalized Gibbs ensembles.

Figure 1

Double occupation $D(t)$ for quenches to (a) $U_{+}=1$, (b) $U_{+}=3$, and (c) $U_{+}=8$, starting from an initial metallic ($U_{-}<2$) or insulating state ($U_{-}>2$); the half-bandwidth is $2V\equiv 2$. In (a) and (b), the internal energy is the same after both quenches. Thick right-pointing arrows mark the double occupation in the thermal state for interaction $U_{+}$ with the same density and internal energy. These values differ from the stationary value $D_{\infty }$, marked by left-pointing arrows, which are approached for large times. The inset in (a) shows a magnification of the large-$t$ behavior.

Figure 2

Stationary $n_{\infty }(ϵ)$ for quenches to (a) $U_{+}=1$ and (b) $U_{+}=3$ [same as in Figs. 1a, 1b], compared to the corresponding thermal values (solid red line). The inset shows a magnification of their differences.