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

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