While ants can be a nuisance, they are actually considered beneficial predators when they are in places where they are not disrupting plant growth. They prefer sandy, dry soils and that is probably why they are in this area. Compost is not an effective means of killing ants, but if a sandy soil is amended with sufficient compost as to make soil more moisture- retentive, ants may move elsewhere.
Ants are difficult to control because colonies are located in chambers many feet below the soil surface. Any control method outside of soil amending, would involve using baits that ants would bring deep into the chambers and share with fellow ants.
A dense turf cover with grass kept 3 inches high or a little higher would go a long way in discouraging ants from an area. Watering to keep soils moist during peak ant activity may encourage ants to relocate.
You may want to choose an area to maintain as a quality turf, and let the ants remain in the rest of the area. See link below for ant control options, many of which include chemical control products, which you can elect not to use.
There is much more information about ant management at the following link: https://extension.umn.edu/insects-infest-homes/ants