We study the correlated Haldane-Hubbard model with single-particle gain and loss, focusing on its non-Hermitian phase diagram and the ensuing nonunitary dynamic properties. The interplay of interactions and nonhermiticity results in insulating behavior with a phase diagram divided into three distinct regions, exhibiting either topologically gapped or (real) gapless regimes and a trivial phase. The latter is mapped by the emergence of a local order parameter associated with a charge density wave. A $\mathcal{P}T$-symmetry breaking at the low-lying spectrum occurs when increasing the gain-loss magnitude at a fixed interaction strength, marking the transition from gapped to gapless topological behavior. Further increase leads to the onset of charge ordering in a first-order phase transition in which level crossing takes place in the spectrum's real part. The support that the staggered gain and loss display to robust charge density wave in equilibrium is confirmed in the real-time dynamics in the presence of nonhermiticity, suggesting that engineered gain and loss can be used to tailor an ordered many-body state in experiments.

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• Mott insulators
• Non-Hermitian systems
• Exact diagonalization
• Hubbard model
• Topology