Quench dynamics and Hall response of interacting Chern insulators

We study the coherent nonequilibrium dynamics of interacting two-dimensional systems after a quench from a trivial to a topological Chern insulator phase. While the many-body wave function is constrained to remain topologically trivial under local unitary evolution, we find that the Hall response of the system can dynamically approach a thermal value of the postquench Hamiltonian, even though the efficiency of this thermalization process is shown to strongly depend on the microscopic form of the interactions. Quite remarkably, the effective temperature of the steady-state Hall response can be arbitrarily tuned with the quench parameters. Our findings suggest a way of inducing and observing low-temperature topological phenomena in interacting ultracold atomic gases, where the considered quench scenario can be realized in current experimental setups.

Figure 1

Thermalization of occupation and Hall response. Upper panels: dynamics of the occupation in the upper band of the postquench Hamiltonian (a) and corresponding dynamical Hall response ${\tilde{\sigma }}_{xy}\left(t\right)$ (b) in the interacting Chern insulator with local interactions only ($V=1$). Lower panels: occupation dynamics (c) and buildup of the Hall response (d) in the Chern insulator including nonlocal interactions ($V_0=1,V_1=0.25V_0$). The results have been obtained within the GKBA, using a $N_k=220\times 220$ grid sampling of the BZ.

Figure 2

Dynamics of the Hall response and orbital pseudospin for a Chern insulator with local interactions only [(a)–(d)] and with nonlocal interactions [(e)–(h)]. The interaction strength is $V=0.65$ [(a) and (c)] and $V=1.0$ [(b) and (d)] in the local case, while for the model with nonlocal interactions it is $V_0=0.65$ [(e) and (g)] and $V_0=1.0$ [(f) and (h)]. We used the GKBA and show results for $N_k=220\times 220$ grid points in the BZ.

Figure 3

Dynamics of the occupation $f_{+}(\mathbf{k};t)$ in the upper band of a quantum spin Hall insulator for (a) $U=1.0,V=0$, and (b) $U=1.5,V=0$. The results have been obtained employing the GKBA. The lower panels depict the nonequilibrium spin Hall conductance for (c) $U=1.0$, (d) $U=1.5$, and (e) $U=2.0$.

Figure 4

Steady-state (spin) Hall conductance of (a) the spinless Chern insulator with nonlocal interactions ($V_1=0.25V_0$) and (b) the spinful ${\mathbb{Z}}_2$ insulator as a function of the ramp time. The GKBA has been used in (a) and (b) for all results, except for $U=2.0$, where the KBE result is shown.