  Log-periodic quantum oscillations discovered in transition-metal
pentatelluride give a clear demonstration of discrete scale invariance (DSI) in
solid-state materials. The peculiar phenomenon is convincingly interpreted as
the presence of two-body quasi-bound states in a Coulomb potential. However,
the modifications of the Coulomb interactions in many-body systems having a
Dirac-like spectrum are not fully understood. Here, we report the observation
of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By
reducing the flakes thickness, the characteristic scale factor is tuned to a
much smaller value due to the reduction of the vacuum polarization effect. The
decreasing of the scale factor demonstrates the many-body effect on the DSI,
which has rarely been discussed hitherto. Furthermore, the cut-offs of
oscillations are quantitatively explained by considering the Thomas-Fermi
screening effect. Our work clarifies the many-body effect on DSI and paves a
way to tune the DSI in quantum materials.
