LAUSR

Considering coupling to a microstructured bath as a relaxation mechanism in a periodically driven dissipative Haldane model, we establish that the system may be tuned to a stroboscopic topological steady state at all finite temperatures. The amplitude and frequency of the periodic drive is so chosen that the Floquet Hamiltonian describing the Haldane model at stroboscopic instants of time in the unitary situation is topologically nontrivial. We establish that in the stroboscopic steady state, the system reaches a thermal state of the Floquet Hamiltonian at a controlled temperature. Further, it is observed that even with a coupling to a bath, remarkably a Chern insulator can indeed be prepared in a Chern nontrivial pure steady state which is expected to exhibit a stroboscopic bulk-boundary correspondence. Using the nonuniqueness of the macroscopic bulk electric polarization of a Chern insulator in its topological phase, we propose a generalized Chern invariant that reflects the topology of out-of-equilibrium many-body stroboscopic states of the Haldane model even in a dissipative ambience. The generalized topology of dynamical Chern insulators being dependent on single-particle correlations is expected to manifest in experiments probing many-body quantum observables.