Topological Mott insulator in the odd-integer filled Anderson lattice model with Hatsugai-Kohmoto interactions

Recently, a quantum anomalous Hall state at odd integer filling in moir\'e stacked MoTe$_2$/WSe$_2$ was convincingly interpreted as a topological Mott insulator state appearing due to strong interactions in {\it band} basis [P. Mai, J. Zhao, B. E. Feldman, and P. W. Phillips, Nat. Commun. {\bf 14}, 5999 (2023)]. In this work, we aim to analyze the formation of a topological Mott insulator due to interactions in {\it orbital} basis instead, being more natural for systems where interactions originate from the character of $f$ or $d$ orbitals rather than band flatness. For that reason, we study an odd-integer filled Anderson lattice model incorporating odd-parity hybridization between orbitals with different degrees of correlations introduced in the Hatsugai-Kohmoto spirit. We demonstrate that a topological Mott insulating state can be realized in a considered model only when weak intra- and inter-orbital correlations involving dispersive states are taken into account. Interestingly, we find that all topological transitions between trivial and topological Mott insulating phases are not accompanied by a spectral gap closing, consistent with a phenomenon called {\it first-order topological transition}. Instead, they are signaled by a kink developed in spectral function at one of the time reversal invariant momenta. We believe that our approach can provide insightful phenomenology of topological Mott insulators in spin-orbit coupled $f$ or $d$ electron systems.