  Planckian behavior has been recently observed in La1.76Sr0.24CuO4 at the
pseudogap critical point. The Planckian behavior takes place in an intriguing
quantum metallic state at a quantum critical point. Here, the Planckian
behavior was simulated with an energy-independent (or flat) and weakly
temperature-dependent electron-boson spectral density (EBSD) function by using
a generalized Allen's (Shulga's) formula. We obtained various optical
quantities from the flat EBSD function, such as the optical scattering rate,
the optical effective mass, and the optical conductivity. These quantities are
well fitted with the recently observed Planckian behavior. Fermi-liquid
behavior was also simulated with an energy-linear and temperature-independent
EBSD function. The EBSD functions agree well with the overall doping- and
temperature-dependent trends of the EBSD function obtained from the optically
measured spectra of cuprate systems, which can be crucial for understanding the
microscopic electron-pairing mechanism for high-Tc superconductivity in
cuprates.
