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We use the term Mott insulator in the broad context of an insulator, which according to band theory calculations should be a metal because there is at least one partially filled band. However, we will primarily consider even-integer filling which could correspond to a band insulator because there is an even number of electrons per unit cell. A more distinct definition of a Mott insulator valid in our case is an insulator in which the electronic charge gap and spin gap are different.
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