I don't think I would dig it up. You probably do have to buy some type of insecticide bait that they bring back into the colony killing the queen.

It might also be a trial and error type thing. The first product you use may not work, but another bait might work.

Since it's in the ground, you could use boiling water. Ants will survive regular water, but an awful lot of boiling water will kill many of them.

Rinse and repeat.