Non-Hermitian Haldane-Hubbard model: effective description of one and two-body dissipations

Using numerically exact diagonalization, we study the correlated Haldane-Hubbard model in the presence of dissipation. Such dissipation can be modeled at short times by the dynamics governed by an effective non-Hermitian Hamiltonian, of which we present a full characterization. If the dissipation corresponds to a two-body loss, the repulsive interaction of the effective Hamiltonian acquires an imaginary component. A competition between the formation of a charge-ordered Mott insulator state and a topological insulator ensues, but with the non-Hermitian contribution aiding in stabilizing the topologically non-trivial regime, delaying the onset of the formation of a local order parameter. Lastly, we analyze the robustness of the ordered phase by following the full dissipative many-body real-time dynamics. An exponentially fast melting of the charge order occurs, whose characteristic rate is roughly independent of the interaction strength, for the case of one-body dissipation.