Chern insulators exhibit fascinating properties, which originate from the topologically nontrivial state characterized by the Chern number. How these properties change if the system is quenched between topologically distinct phases is, however, not fully understood. In this paper, we investigate the quench dynamics of the prototypical massive Dirac model for topological insulators in two dimensions. We consider both dissipationless dynamics and the effect of electron-phonon interactions, and ask how the transient dynamics and nonequilibrium steady states affect simple observables. Specifically, we discuss a time-dependent generalization of the Hall effect and the dichroism of the photoexcitation probability between left and right circularly polarized light. We present optimized schemes based on these observables, which can reveal the evolution of the topological state of the quenched system.
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.
Interactions generically have important effects on topological quantum phases. For a quantum anomalous Hall (QAH) insulator, the presence of interactions can qualitatively change a topological phase diagram, which, however, is typically hard to measure in an experiment. Here we propose a scheme based on quench dynamics to detect the mean-field topological phase diagram of an interacting Chern insulator described by the QAH-Hubbard model, with nontrivial dynamical quantum physics being uncovered. We focus on the dynamical properties of the system at a weak to intermediate Hubbard interaction, which mainly induces a ferromagnetic order under the mean-field level. Remarkably, three characteristic times---
ts,tc, and
t∗---are found in the quench dynamics. The first two (
ts,tc) capture the emergences of dynamical self-consistent particle density and the dynamical topological phase transition, respectively, while the third one (
t∗) gives a linear scaling time on the topological phase boundaries. We show generically that the characteristic times obey
ts>t∗>tc (
t∗<ts<tc) in the repulsive (attractive) interacting regime, when the system is quenched from an initial nearly fully polarized state to the topologically nontrivial regimes. Moreover, the Chern number of the equilibrium phase of postquench interacting Hamiltonian can be determined by any two of the three timescales, providing a dynamical way to determine the equilibrium mean-field topological phases. Experimentally, the measurement of
ts is challenging, while
tc and
t∗ can be directly read out by measuring the spin polarizations of four Dirac points and the time-dependent particle density, respectively, showing the feasibility of the present dynamical scheme. Our work opens a way to detect by quench dynamics the mean-field phase diagram of Chern insulators with interactions.
We investigate the transport properties of Chern insulators following a quantum quench between topological and nontopological phases. Recent works have shown that this yields an excited state for which the Chern number is preserved under unitary evolution. However, this does not imply the preservation of other physical observables, as we stressed in our previous work. Here we provide an analysis of the Hall response following a quantum quench in an isolated system, with explicit results for the Haldane model. We show that the Hall conductance is no longer related to the Chern number in the postquench state, in agreement with previous work. We also examine the dynamics of the edge currents in finite-size systems with open boundary conditions along one direction. We show that the late-time behavior is captured by a Generalized Gibbs Ensemble, after multiple traversals of the sample. We discuss the effects of generic open boundary conditions and confinement potentials.
We study the Hall conductance of a Chern insulator after a global quench of the Hamiltonian. The Hall conductance in the long time limit is obtained by applying the linear response theory to the diagonal ensemble. It is expressed as the integral of the Berry curvature weighted by the occupation number over the Brillouin zone. We identify a topologically driven nonequilibrium phase transition, which is indicated by the nonanalyticity of the Hall conductance as a function of the energy gap
mf in the post-quench Hamiltonian ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{f}$. The topological invariant for the quenched state is the winding number of the Green's function
W, which equals the Chern number for the ground state of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{f}$. In the limit ${m}_{f}\ensuremath{\rightarrow}0$, the derivative of the Hall conductance with respect to
mf is proportional to
ln∣mf∣, with the constant of proportionality being the ratio of the change of
W at
mf=0 to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb model in the fermionic basis.
We investigate the nonequilibrium dynamics of the spinless Haldane model with nearest-neighbor interactions on the honeycomb lattice by employing an unbiased numerical method. In this system, a first-order transition from the Chern insulator at weak coupling to the charge-density-wave (CDW) phase at strong coupling can be characterized by a level crossing of the lowest energy levels. Here we show that if adiabatically following the eigenstates across this level crossing, their Chern numbers are preserved, leading to the identification of a topologically nontrivial low-energy excited state in the CDW regime. By promoting a resonant energy excitation via an ultrafast circularly polarized pump pulse, we find that the system acquires a nonvanishing Hall response as a result of the large overlap enhancement between the time-dependent wave function and the topologically nontrivial excited state. This response is suggestive of a photoinduced topological phase transition via unitary dynamics, despite a proper definition of the Chern number remaining elusive for an out-of-equilibrium interacting system. We contrast these results with more common quench protocols in which such features are largely absent in the dynamics even if the postquench Hamiltonian displays a topologically nontrivial ground state.
We perform a sudden quench on the Haldane model with long range interactions, more specifically generalizing to the next to next nearest neighbor hopping, referred to as the
N3 model in our work. Such a model possesses both isotropic and multiple anisotropic (satellite) Dirac points which lead to a rich topological phase diagram consisting of phases with higher Chern number
(C). Quenches between the topological and the nontopological phases of such an infinite system probe the effect of the presence of the anisotropic Dirac points on the nonequilibrium response of the topological system. Interestingly, the Chern number remains the same before and after the quench for both the quenching protocols, even when the quench of the system is carried out between two different topological phases. However, for a finite system, we establish that the initial edge current asymptotically decays to zero when the system is quenched to the nontopological phase although the Chern number for the corresponding periodically wrapped system remains unaltered; what is remarkable is that when the Hamiltonian is quenched from
∣C∣=2 phase to the nontopological phase the edge current associated with the inner channel decays at a faster rate than the outer channel resembling a situation in which the system passes through the phase with
∣C∣=1 before ending up in the phase
C=0.