You did not describe the ants or how they are killing your plants. Identification is necessary for proper control of any pest. Contact your local Extension office and inquire about diagnostic services.
Ants are generally beneficial insects. There are several ants that nest in the soil and, depending upon the species, their nests can be small and inconsequential or amazingly large mounds. Unless the mounds are harming garden beds, in the way of garden work, harming the grass, interfering with the lawn mower, or in an area where children play, it is best to leave them alone. The field ant builds very large, raised mounds that can upset roots of plants, take up a lot of garden space, and perhaps be a problem to gardeners. Most field ants are black, but many are reddish brown; they are moderately large and sometimes mistaken for carpenter ants. Field ants live in moderately sized colonies and are beneficial scavengers. They feed on other insects, nectar from flowers, and honeydew from aphids.
If you have a large field ant mound in your garden, it will be very difficult to eliminate. The queen must be killed or relocated to truly manage an ant colony; however, there may be more ants ready to replace them. Try raking the mound flat regularly and often. Wear protective clothing - field ants can bite when defending their nest; otherwise, they are not aggressive. Repeated drenchings of the nest with an insecticidal soap solution is sometimes effective in forcing an ant colony to relocate. Boiling water, used at about 3 gallons per mound, can eliminate some ant colonies. Try it on a cool, sunny morning, when the ants are near the soil surface.
Consider the connection between ants and aphids. Many soil-nesting ants feed on honeydew secreted by aphids. The ants even "tend" and protect the aphids to maintain the sweet food source they crave. If the aphids are controlled, the ant problem may be eliminated. Might there be plants infested with aphids providing food for the ants? If you determine that aphids are feeding on your vegetables and you look for an insecticide to control them (or the ants) be sure the product is meant to be used on vegetables and follow all directions carefully.
