Multiband Superconductivity in the Exactly Solvable Hatsugai-Kohmoto Model

Multiband superconductivity gives rise to a rich landscape of possible pairing states. Here we study superconductivity in the multiband extension of the Hatsugai-Kohmoto model, an exactly solvable model of correlated electrons with momentum-local interactions, which provides a minimal framework to explore the interplay of strong correlations, orbital structure and pairing symmetry. Focusing on a two-orbital system with point-group symmetry $\rm D_{4h}$, we classify the symmetry-allowed superconducting gap structures, taking into account spin, orbital and momentum degrees of freedom. We further compute the critical temperature and the superconducting order parameter for selected pairing channels as functions of interaction and pairing strength within a mean-field treatment. Our results provide a systematic framework for analyzing superconductivity in the orbital Hatsugai-Kohmoto model and extend symmetry-based approaches to correlated multiband settings.