Integrable Mott Insulators Driven by a Finite Electric Field

We develop a method for extracting the steady nonequilibrium current from studies of driven isolated systems, applying it to the model of a one-dimensional Mott insulator at high temperatures. While in the nonintegrable model the nonequilibrium conditions can be accounted for by internal heating, the integrability leads to a strongly nonlinear dc response with a vanishingly small dc conductivity in the linear-response regime. The finding is consistent with equilibrium results for the dc limit of the optical conductivity determined in the presence of a weak and decreasing perturbation.

Figure 1

Nonintegrable case $V=3$, $W=1$, $L=26$ with a pure initial state $N_s=1$. (a) Current $I(t)$ (main) and $I(t)/F$ (inset) for initial ${\beta }_{\mathrm{eff}}\simeq 0.42$. (b),(c) $I/F$ vs ${\beta }_{\mathrm{eff}}$ for various initial energies $E_0$ and various $F$, respectively; (d) The same as in (c) but for various $L$. The equilibrium LR results are shown in (c) for comparison.

Figure 2

(a),(b) $I/F$ vs ${\beta }_{\mathrm{eff}}$ for integrable system $V=3$, $W=0$, and $L=28$. (c),(d) ${\beta }_{\mathrm{eff}}$ vs $t{F}^2$ for integrable (c) and nonintegrable (d) systems. In (c) curves are shifted horizontally so they overlap for large times. $N_s=1$ apart from $F=0.1$ and $F=0.2$ in (a) where $N_s=7$.

Figure 3

$I/({\beta }_{\mathrm{eff}}F)$ estimated from $E(t)$ [Eq. (2)] for ${\beta }_{\mathrm{eff}}\to 0$ (points with guidelines) and LR for $W=1$ (dotted line). For $W=1$ the dashed line is a fitted parabola.

Figure 4

Equilibrium LR: $\sigma (\omega )/\beta$ in the limiting case $\beta \to 0$ for various $W$ (a) and various system sizes $L$ (b). (c) $\sigma (0)/\beta$ vs $1/L$ (points), (d) $W$ dependence of $\sigma (0)/\beta$ extrapolated to $L\to \infty$.