  For an extended Harper model, the fidelity for two lowest band edge states
corresponding to different model parameters, the fidelity susceptibility and
the von Neumann entropy of the lowest band edge states, and the
spectrum-averaged von Neumann entropy are studied numerically, respectively.
The fidelity is near one when parameters are in the same phase or same phase
boundary; otherwise it is close to zero. There are drastic changes in fidelity
when one parameter is at phase boundaries. For fidelity susceptibility the
finite scaling analysis performed, the critical exponents $\alpha$, $\beta$,
and $\nu$ depend on system sizes for the metal-metal phase transition, while
not for the metal-insulator phase transition. For both phase transitions
$\nu/\alpha\approx2$. The von Neumann entropy is near one for the metallic
phase, while small for the insulating phase. There are sharp changes in von
Neumann entropy at phase boundaries. According to the variation of the
fidelity, fidelity susceptibility, and von Neumann entropy with model
parameters, the phase diagram, which including two metallic phases and one
insulating phase separated by three critical lines with one bicritical point,
can be completely characterized, respectively. These numerical results indicate
that the three quantities are suited for revealing all the critical phenomena
in the model.
