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For an extended Harper model, the fidelity for two lowest band edge statescorresponding to different model parameters, the fidelity susceptibility andthe von Neumann entropy of the lowest band edge states, and thespectrum-averaged von Neumann entropy are studied numerically, respectively.The fidelity is near one when parameters are in the same phase or same phaseboundary; otherwise it is close to zero. There are drastic changes in fidelitywhen one parameter is at phase boundaries. For fidelity susceptibility thefinite scaling analysis performed, the critical exponents $\alpha$, $\beta$,and $\nu$ depend on system sizes for the metal-metal phase transition, whilenot for the metal-insulator phase transition. For both phase transitions$\nu/\alpha\approx2$. The von Neumann entropy is near one for the metallicphase, while small for the insulating phase. There are sharp changes in vonNeumann entropy at phase boundaries. According to the variation of thefidelity, fidelity susceptibility, and von Neumann entropy with modelparameters, the phase diagram, which including two metallic phases and oneinsulating phase separated by three critical lines with one bicritical point,can be completely characterized, respectively. These numerical results indicatethat the three quantities are suited for revealing all the critical phenomenain the model.

Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model