Dielectric Breakdown in Spin-Polarized Mott Insulator

Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin-polarized insulator the decay rate of the ground state into excited holon-doublon pair can be evaluated numerically as well to high accuracy analytically. Results show that the threshold field depends on the charge gap as $F_{\mathrm{th}}\propto {\Delta }^{3/2}$. Numerical results on small systems indicate on the persistence of a similar mechanism for the breakdown for decreasing magnetization down to unpolarized system.

Figure 1

Energy levels $E_n$ (in units of $t$) vs phase $\varphi$ in the system with $L=21$ sites and $U=4$. Thick line represents the g.s. and the effective holon-doublon pair state dispersion.

Figure 2

Ground state weight $\ln |a_0{|}^2$ vs time $\tau /{\tau }_B$ for $U=4$ and different fields $F=0.2–0.5$. For $F=0.5$ comparison of results for smoothly and instantaneously switched $F(\tau )$ is presented while for $F<0.5$ only smooth switching is used.

Figure 3

Ground state decay rate $\Gamma$ (log scale) vs $1/F$ for $U=4$ as evaluated by direct numerical solution of TDSE (full line), decay into free HD states, numerically integrating Eq. (7) (dotted), and analytical expression, Eq. (9) (dashed).

Figure 4

Normalized g.s. weight $(1/N_d)\ln |a_0{|}^2$ vs time $\tau /{\tau }_B$ for (a) $U=4$ and fields $F=0.3$, 0.6, 0.8, (b) $U=10$ and $F=1.6$, 2.2, 2.6, for various spin states $1\le N_d\le L/2$.

Figure 5

Threshold field $F_{\mathrm{th}}$ vs charge gap $\Delta$ for different magnetizations $m\sim 1/2$ (given by $N_d=1$) and $m=1/4$, 0 as obtained numerically for $L=16$. Full curve (HD) represent the analytical approximation, Eq. (9), while the dashed curve is the LZ approach result from Ref. 9.