Collective excitations in one-dimensional ultracold Fermi gases: Comparative study

Time-dependent density-functional theory (TDDFT) is a powerful tool in studying the nonequilibrium dynamics of inhomogeneous interacting many-body systems. Here we show that the simple adiabatic local-spin-density approximation for the time-dependent exchange-correlation potential is surprisingly accurate in describing collective density and spin dynamics in strongly correlated one-dimensional ultracold Fermi gases. Our conclusions are based on extensive comparisons between our TDDFT results and accurate results based on the adaptive time-dependent density-matrix renormalization-group method.

Figure 1

(Color online) Charge $n_i\left(t\right)$ and spin $s_i\left(t\right)$ occupations as functions of lattice site $i$ and time $t$ for $L=72$ (the hard-wall boundary conditions are imposed at the sites 0 and 73), $N_{\uparrow }=N_{\downarrow }=14$, $u=+2$, $W_{\uparrow }/\gamma =W_{\downarrow }/\gamma =-7/18$, and $w=2$. TDDFT data (filled circles and squares) are compared with tDMRG data ($\times$ and $+$). Top left panel: ground-state charge and spin occupations for times $t\le 0$. Top right panel: same as in the top left panel but at time $t=5\hslash /\gamma$. Bottom left panel: same as in the top panels but at time $t=10\hslash /\gamma$. Bottom right panel: same as in the bottom left panel but at time $t=15\hslash /\gamma$.

Figure 2

(Color online) Same as in Fig. 1 but for $t=20\hslash /\gamma$ (top panel) and $t=30\hslash /\gamma$ (bottom panel).

Figure 3

(Color online) Same as in Fig. 1 but for $N_{\uparrow }=20$, $N_{\downarrow }=8$, $u=+2$, $W_{\uparrow }/\gamma =W_{\downarrow }/\gamma =-5/9$, and $w=2$.

Figure 4

(Color online) Same as in Fig. 1 but for $u=+4$.

Figure 5

(Color online) Same as in Fig. 3 but for $u=+4$.

Figure 6

(Color online) Top panels: Charge $n_i\left(t\right)$ and spin $s_i\left(t\right)$ occupations as functions of lattice site $i$ and time $t$ for $L=72$, $N_{\uparrow }=N_{\downarrow }=14$, $u=+6$, $W_{\uparrow }/\gamma =W_{\downarrow }/\gamma =-7/18$, and $w=2$. TDDFT data (filled circles and squares) are compared with tDMRG data ($\times$ and $+$). Left: ground-state charge and spin occupations for times $t\le 0$. Right: same as in the left panel but at time $t=6\hslash /\gamma$. Bottom panels: same in the top panels but for $N_{\uparrow }=20$ and $N_{\downarrow }=8$.