marking post
桓 centers on a wooden post used for marking or as a pillar, specifically a marking post.
桓 combines 木 (tree/wood) with 亘, which likely contributes the sound. The character refers to a wooden post or pillar used as a marker.
The left side is a tree 木, and the right side 亘 looks like a post extending across. Picture a wooden marking post standing firmly in the ground.
For カン, imagine a can placed on top of a wooden marking post: can -> カン, and the post marks the spot.
—