Nonequilibrium Quantum Dynamics of a Charge Carrier Doped into a Mott Insulator

We study real-time dynamics of a charge carrier introduced into an undoped Mott insulator propagating under a constant electric field $F$ on the $t\mathrm{\text{−}}J$ ladder and a square lattice. We calculate the quasistationary current. In both systems an adiabatic regime is observed followed by a positive differential resistivity (PDR) at moderate fields where the carrier mobility is determined. Quantitative differences between the ladder and two-dimensional (2D) systems emerge when at large fields both systems enter the negative differential resistivity (NDR) regime. In the ladder system Bloch-like oscillations prevail, while in two dimensions the current remains finite, proportional to $1/F$. The crossover between the PDR and NDR in two dimensions is accompanied by a change of the spatial structure of the propagating spin polaron.

Figure 1

Ladder with $L$ rungs: (a) increase of energy $\Delta E(t)$ in different regimes; (b) real-time current $j(t)$ normalized by kinetic energy $a(t)=j(t)/(F|E_{kx}(t)|)$ (note the steady $F$-independent ratio); (c) kinetic energy $E_{kx}$ vs $t/t_B$ (inset) and $t/L{t}_B$ (main); (d) steady current $\overline{j}$ vs $F$. Dotted line in (a) shows $\Delta E(t)$ estimated from the mobility $\mu$ shown in (d) as linear fits $\overline{j}=\mu F$. $J=0.6$ is used in (a)–(c).

Figure 2

2D lattice: (a) increase of energy $\Delta E(t)$ for $J=0.3$, various $F$ (main) and $N_h=12$, 13, 14 (inset); (b) real-time current $j(t)$, $\overline{j}$ from Eq. (3) (dotted-dashed lines); (c) steady current $\overline{j}$ vs $F$ fitted by $\overline{j}=\mu F$ (dashed lines) and $\overline{j}=b/F$ (solid lines) in PDR and NDR regimes, respectively.

Figure 3

2D lattice with $J=0.3$. Snapshots of the spin deformation $C(\mathbf{r})$ in the vicinity of hole [placed at (0,0)], taken at different times $t/t_B$. Solid arrows indicate direction of the electric field.