Construct order parameter from the spectra of mutual information

In this paper, we try to establish a connection between a quantum information concept, i.e. the mutual information, and the conventional order parameter in condensed matter physics. We show that a non-vanishing mutual information at a long distance means the existence of long-range order. By analyzing the entanglement spectra of the reduced density matrix that are used to calculate the mutual information, we show how to find the local order operator used to identify various phases with long-rang order.