a government under the strict control of a Caliph, a single spiritual leader

an ideal Islamic polity governed by God's law

The administration of a Caliph, title of Islamic empire. Ar.

A caliphate (Arabic خلافة) is an Islamic federal government representing the political unity of the Muslim world despite theological differences, with the head of state (caliph) as the heir of Muhammad's political, not religious, authority. From the time of Muhammad until 1924, it provided varying degrees of unity among the diverse nations that adopted Islam. The caliphate is the only form of government that has full approval in early Islamic theology, and "is the core political concept of Sunni Islam, by the consensus of the Muslim majority in the early centuries."