We have had a lot of large ant colonies in our raised beds, for example among the tomato plants. One non-toxic method to diminish the colony or make it move is to introduce ants from another ant nest. I push a shovel into a big ant nest, get a bunch of ants, and put it onto the nest I want to eliminate.
The ants start fighting right away. It's a little gruesome; sometimes a few hours later we can see the mangled bodies of the "invaders" strewn around the top of the nest. But I've found if I do this a couple of times, the original nest seems to disappear, or moves off to some place where it doesn't bother the garden.
I read about this somewhere - maybe NAFEX? It does seem to work pretty well for us.