Mix about 3% by weight boric acid powder (harmless other than to insects, even used as an eyewash solution) with powdered sugar (sucrose), ideally confectioners or other very finely powdered sugar. Many common anti-ant pesticide products contain boric acid or equivalent. A container of boric acid, which any drug store should have, likely at least 100 g, and a bag of sugar will last many years.
Spread little piles or lines (not big enough to be interest to mice, rats, etc.), about every six feet around the area you want to protect or get rid of the ants. To ants, this near pure sugar is like rocket fuel. They take it back, feed on it and it's a cumulative poison. If you notice piles are gone, put out more, it takes about a week for the ants to get their fill, the stuff to work, and for them to disappear. If it rains, you'll need to put out more, but the stuff costs like nothing. And you can also make thick solutions of the mixed powder and fill aluminum foil or other small containers. You can use this indoors too. And I presume a simple mixture of natural boric acid and common sugar would be considered fully "organic."
Read more about it. I presume boric acid is a good place to start. And if the ants don't like the sugar bait, try mixing boric acid (or solution) with some fatty or protein-rich bait.