# Long/short range order v.s. long/short range interactions v.s. long-short range entanglement

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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.

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