Nonequilibrium Propagation and Decay of a Bound Pair in Driven $t\mathrm{\text{−}}J$ Models

We perform an accurate time-dependent numerical study of an out-of-equilibrium response of a bound state within $t\mathrm{\text{−}}J$ systems on a two-leg ladder and a square lattice. We show that the bound hole pair decays with the onset of finite steady current if both mechanisms for binding and the dissipation share matching degrees of freedom. Moreover, by investigating the mechanism of decay on the square lattice we find that the dynamics is governed by the decay in the direction perpendicular to the electric field, leading to much shorter decay times in comparison to the ladder where such dynamics is topologically restricted.

Figure 1

Time evolution on a $2\times 10$ ladder with two holes under constant $F$ switched on at $t=0$. (a) $d_{\Vert }(t)$ vs $E(t)$ for $J_{\perp }=1$ (along the rungs), $J_{\parallel }=0.4$ (along the legs) and various $F$. (b) $x(t)$ (main) and $d_{\Vert }(t)$ vs $x(t)$ (inset) for three different values of $V$ and $W$. We use $J_{\perp }=J_{\parallel }=0.4$ and $F=0.125$ in (b). In the inset, $d_{\Vert }(t)$ is not subtracted by $d_{\Vert }(t=0)$; thin dashed horizontal line shows $d_{\parallel }$ for two noninteracting fermions.

Figure 2

Driven hole pair on the square lattice. (a) $d_{\Vert }(t)$ and $d_{\perp }(t)$ for $J=0.4$ and $F=0.7$. (b) $d_{\perp }(t)J$ vs $x(t)J$ for different $J$ and $F$. Black solid line represents a fit $d_{\perp }(t)=\beta x(t)\exp (-\frac{1}{\alpha Jx(t)})$, where $\beta =1.474$ and $\alpha =2.066$. (c) Current $j(t)$ for different $J$ and $F$. (d) $\xi (t)$ vs $x(t)$, see Eq. (6), for the same set of parameters as in (b).

Figure 3

$\mathcal{C}(\mathbf{r})$ measuring time-dependent probability for the hole pair to be at a relative position $\mathbf{r}$, fulfilling the sum rule $\sum _{\mathbf{r}}\mathcal{C}(\mathbf{r})=1$. Arrows mark direction of electric field. We set $J=0.4$ and $F=0.7$.