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In this work, we propose an exactly solvable two-dimensional lattice model ofstrongly correlated electrons that realizes a quantum anomalous Hall insulatorwith Chern number $\mathcal{C}=1$. First, we show that the interplay of ionicpotential, Rashba spin-orbit coupling and Zeeman splitting leads to theappearance of quantum anomalous Hall effect. Next, we calculate in an exactmanner Chern number for the correlated system where electron-electroninteractions are introduced in the spirit of Hatsugai-Kohmoto model using twocomplementary methods, one relying on the properties of many-body groundstateand the other utilizing single-particle Green's function, and subsequently wedetermine stability regions. By leveraging the presence of inversion symmetrywe find boundaries between topological and trivial phases on the analyticalground. Notably, we show that in the presence of correlations onset oftopological phase is no longer signalled by a spectral gap closing consistentlywith phenomenon called in literature as {\it first-order topologicaltransition}. We provide a clear microscopic understanding of this inherentlymany-body feature by pinpointing that the lowest energy excited states in thecorrelated system are no longer of the single-particle nature and thus are notcaptured by a spectral function.

Quantum anomalous Hall insulator in ionic Rashba lattice of correlated electrons