Nonequilibrium dynamics in pumped Mott insulators

We use time-evolution techniques for (infinite) matrix product states to calculate, directly in the thermodynamic limit, the time-dependent photoemission spectra and dynamic structure factors of the half-filled Hubbard chain after pulse irradiation. These quantities exhibit clear signatures of the photoinduced phase transition from insulator to metal that occurs because of the formation of so-called $\eta$ pairs. In addition, the spin dynamic structure factor loses spectral weight in the whole momentum space, reflecting the suppression of antiferromagnetic correlations due to the buildup of $\eta$-pairing states. The numerical method demonstrated in this work can be readily applied to other one-dimensional models driven out of equilibrium by optical pumping.

Figure 1

Contour plots of $\tilde{P}(\pi ,t=15t_{\mathrm{h}}^{-1})$ (a) and ${\tilde{P}}_{r>0}(\pi ,t=15t_{\mathrm{h}}^{-1})$ (b) in the ${\omega }_{\mathrm{p}}\text{−}{A}_0$ plane for an infinite Hubbard chain with $U/t_{\mathrm{h}}=8$ at half filling. The pump pulse has width ${\sigma }_{\mathrm{p}}=2$ and is centered at time $t_0·t_{\mathrm{h}}=10$.

Figure 2

Snapshots of the photoemission spectra $A^{-}(k,\omega ;t)$ for the $\eta$-pairing non-dominant (left panels with ${\omega }_{\mathrm{p}}/t_{\mathrm{h}}=4$) and dominant (right panels with ${\omega }_{\mathrm{p}}/t_{\mathrm{h}}=7$) states during the pump at $t·t_{\mathrm{h}}=5$ [(a) and (d)], 10 [(b) and (e)], and 15 [(c) and (f)]. The data are obtained by the (i)TEBD technique with IBCs at $U/t_{\mathrm{h}}=8$, where the pump is parametrized by $A_0=4$ and ${\sigma }_{\mathrm{p}}=2$ at $t_0·t_{\mathrm{h}}=10$.

Figure 3

The transient integrated density of states $A^{-}(\omega ;t)$ from Eq. (7) for $U/t_{\mathrm{h}}=8$ with ${\omega }_{\mathrm{p}}/t_{\mathrm{h}}=4$ (a) and 7 (b). The pump is parametrized as in Fig. 2.

Figure 4

Snapshots of the dynamic structure factors for spin [$S_{\mathrm{s}}(q,\omega ;t)$] and charge [$S_{\mathrm{c}}(q,\omega ;t)$] during the pump at $t·t_{\mathrm{h}}=5$ [(a) and (d)], 10 [(b) and (e)], and 15 [(c) and (f)]. The data are obtained by the time-evolution technique with IBCs, where the pump is parametrized by $A_0=0.4$ and ${\omega }_{\mathrm{p}}/t_{\mathrm{h}}=7$ (‘+’ symbol in Fig. 1).

Figure 5

The time-dependent charge structure factor $S_{\mathrm{c}}(q;t)$ for ${\omega }_{\mathrm{p}}/t_{\mathrm{h}}=7$ obtained from the energy-integrated $S_{\mathrm{c}}(q,\omega ;t)$ (symbols) and the Fourier transform of $\langle \psi \left(t\right)\left|{\widehat{\eta }}_{j+r}^z{\widehat{\eta }}_j^z\right|\psi \left(t\right)\rangle$ [Eq. (8)] (lines), where the pump is parametrized as in Fig. 4.