Oral:Chaotic-Integrable Transition for Disordered Orbital Hatsugai-Kohmoto Model

We have drawn connections between the Sachdev-Ye-Kitaev model and the multi-orbit Hatsugei-Kohmoto model, emphasizing their similarities and differences regarding chaotic behaviors. In contrast to the Sachdev-Ye-Kitaev model, the quartic term in the disordered orbital Hatsugei-Kohmoto model does not independently generate chaotic behavior. However, when both quadratic and quartic random terms are present, chaotic behaviors emerge, as demonstrated through adjacent gap ratio and spectral form factor analysis. The feature of the spectral form factor, such as the ramp-plateau structure, along with the adjacent gap ratio, are indicative of chaos in the disordered orbital Hatsugei-Kohmoto model. Early-time behavior of the out-of-time-order correlator also supports this chaotic characterization, while its late-time saturation exhibits a temperature dependence. One significant conclusion is that the plateau value of the out-of-time-order correlator, whether in the Hatsugei-Kohmoto model, Sachdev-Ye-Kitaev model with two- or four-body interactions, or a disorder-free Sachdev-Ye-Kitaev model, does not seem to 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.