Does divorce take effect through a phrase that conveys its meaning, such as saying: "This is a separation between me and you," whether one intended divorce by it or not, or does it only take effect through the explicit word of divorce, according to the Hanafi school of thought?

Divorce occurs through an explicit utterance or through an ambiguous phrase (kinayah) that could imply divorce. An explicit utterance does not require an intention for the divorce to take effect. As for an ambiguous phrase, divorce does not occur through it unless there is an intention or something that stands in its place.

So, the husband's statement to his wife: "This is a separation between me and you" is an ambiguous phrase that could imply divorce or something else. If the husband intended divorce by it, then it takes effect; otherwise, it does not.