I'm sorry I can't help but wow, that is one of the strangest problems I have ever heard of.
Was there a clause about the house being haunted when you closed?
Even if there was a leak, an ant can't possibly swim in 100+ PSI of water... scratch that, an ant cant really swim to begin with. At least not in an enclosed area with no air.
Now is this one of
these? Maybe there's actually a way they are getting into the faucet part itself. Maybe a small crack in a tile or something or whatever is behind it.