Chaotic-Integrable Transition for Disordered Orbital Hatsugai-Kohmoto Model

YingLin Li^1*, PoYao Chang¹, ChenTe Ma²

¹Physics, National Tsing Hua University, Hsing Chu City, Taiwan
²Physics and Astronomy, Iowa State University, Ames, Iowa, USA

* Presenter:YingLin Li, email:s1012424@gmail.com

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. The features of spectral form factor, such as the dip-ramp-plateau structure, along with the adjacent gap ratio, are indicative of chaos in the disordered orbital Hatsugei-Kohmoto model. The out-of-time-order correlator also supports this chaotic characterization, while its late-time saturation exhibits a consistent 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 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 that 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.

Keywords: Quantum Chaos, Hatsugei-Kohmoto model, Sachdev-Ye-Kitaev model