Chaotic-Integrable Transition for Disordered Orbital Hatsugai-Kohmoto Model

We have drawn connections between the Sachdev-Ye-Kitaev model and the multi-orbit Hatsugai-Kohmoto model, emphasizing their similarities and differences regarding chaotic behaviors. The features of the spectral form factor, such as the dip-ramp-plateau structure and the adjacent gap ratio, indicate chaos in the disordered orbital Hatsugai-Kohmoto model. One significant conclusion is that the plateau value of the out-of-time-order correlator, whether in the Hatsugai-Kohmoto model, Sachdev-Ye-Kitaev model with two- or four-body interactions, or a disorder-free Sachdev-Ye-Kitaev model, does not effectively differentiate between integrable and chaotic phases in many-body systems. This observation suggests a limitation in using out-of-time-order correlator plateau values as a diagnostic tool for chaos. Our exploration of these ideas provides a deeper understanding of how chaos arises in non-Fermi liquid systems and the tools we use to study it. It opens the door to further questions, particularly about whether there are more effective ways to distinguish between chaotic and integrable phases in these complex systems.