Notes on Quantum oscillation for Hatsugai-Kohmoto model

Motivated by the non-Fermi liquid (NFL) phase in solvable Hatsugai-Kohmoto (HK) model and ubiquitous quantum oscillation (QO) phenomena observed in strongly correlated electron systems, e.g. cuprate high-Tc superconductor and topological Kondo insulator SmB$_{6}$, we have studied the QO in HK model in terms of a combination of analytical and numerical calculation. In the continuum limit, the analytical results indicate the existence of QO in NFL state and its properties can be described by Lifshitz-Kosevich-like formula. Furthermore, numerical calculations with Luttinger's approximation on magnetic-field-dependent density of state, magnetization and particle's density agree with the findings of analytical treatment. Although numerical simulation from exact diagonalization exhibits certain oscillation behavior, it is hard to extract its oscillation period and amplitude. Therefore, more work (particularly the large-scale numerical simulation) on this interesting issue is highly desirable and we expect the current study on HK model will be helpful to understand generic QO in correlated electron materials.