The following terms have been widely used to characterized the phases of quantum matter or the gauge theory:
i. Long/short range order,
ii. long/short range interactions,
iii. long-short range entanglement
How are they different from each other?
Can one give examples for certain phases of matter that has long/short range order, long/short range interactions, long-short range entanglement for each choices of long/short? There are totally $2^3=8$ possible characterizations in terms of these terms.