  We present the evolution of quantum correlation in the quantum energy
teleportation (QET) protocol using quantum discord, instead of the
traditionally used entanglement entropy. In the QET protocol, where local
observations and conditional operations are repeated, quantum correlations
become nontrivial because of the statistical creation of mixed states. In this
paper, we use quantum discord as a measure of quantum correlation in mixed
states and investigate its relationship to teleported energy and phase
transitions. During the process of Alice and Bob performing QET, one would
expect that the entanglement between Alice and Bob is completely broken by
Alice's measurement of the quantum state, and thus the quantum correlation
disappears. However, contrary to this expectation, it is shown using quantum
discord that the quantum correlation does not disappear during the entire
process of QET. To demonstrate the robustness of the quantum correlation in QET
at various phase structures, we perform the numerical analysis using several
benchmark models including the Nambu-Jona-Lasino (NJL) model with both the
chiral chemical potential and the chemical potential, which are useful to study
the phase structures mimicking the chiral imbalance between left- and right-
quarks coupled to the chirality density operator. In all cases we studied, the
quantum discord behaved as an order parameter of the phase transition.
