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We study the ground-state phase diagram of a Bose-Fermi mixture loaded in aone-dimensional optical lattice by computing the ground-state fidelity andquantum entanglement. We find that the fidelity is able to signal quantum phasetransitions between the Luttinger liquid phase, the density-wave phase, and thephase separation state of the system; and the concurrence can be used to signalthe transition between the density-wave phase and the Ising phase.

Phase diagram of a Bose-Fermi mixture in a one-dimensional optical lattice in terms of fidelity and entanglement