Natural ant control presupposed the ants are in the house. Ants in the garden are doing their job and while they may be unsightly, they are part of nature's design. They're actually like little vacuum cleaners, sucking up bits of fungus and garden detritus that would otherwise act as a food source for bad guys.
Ants in the garden are cleaning up the fungus, they do not create the fungal problems or dead plants. Think of them as nature's clean up crew taking advantage of the damage done by other diseases and insects
And no, they don't cause peonies to open (they're there sucking up the sweet sap from the buds) and peonies will open nicely with or without them.
If you have ants in the lawn,
Simply mow the grass higher. You won't see the ant hills and both you and the ants will be happier. They'll keep cleaning up the fungus and other problems that you'll never see.
Keep knocking down the hills. They get the message, Or pour boiling water down the hill (slowly) and again, the survivors get the message. This is an ongoing battle. Remember that all that sand and stone protection is an excellent housing situation for the ants so you'll have to be persistent in this kind of natural ant control.
There is no "one stop chemical cure" for ants unless it is extremely toxic and persistent (stays around a long time) and you don't want anything like that to sit on or have a kid or pet crawl on. You'd track the material into the house on the soles of your shoes and that too is not a good idea so persistence and some of the following recipes will work.
Add borax to sugar. The oft quoted concentration is 50:50 but if you start with that, the ants will not likely be too fond of it.
Start with a much lower concentration of borax maybe 10% and very gradually increase it to 30-40%. The objective is to have the ants take as much borax as possible into the nest and they'll take it if it is sweet. Put it where you see the ants or on the ant trails.
I've used borax successfully in the house
Ants follow "trails" left by other ants so that's why you'll see them in a line. If you put the food on the trail, they'll find it. Others will go around it but soon you'll have a line straight for your food source.
Apparently baby powder or talcum powder is not appreciated. I'm told if you dust the ants and the trail, they'll stop coming.
I have used vinegar to destroy their trails and if you can get it close to the source, they'll get confused and not come in for a while. I used it at full strength but some folks have diluted it with water. The other benefit to this of course is that it cleans the counters etc as you wipe out the ant trails.
I'm told that some gardeners have had great luck simply spraying the ant areas their trail, their entry points etc with insecticidal soap. Some have reported that ivory soap works very well too.
Diatomaceous earth will cut up ants as quickly as it cuts up other small insects. You can scatter this around and it is not dangerous to humans or pets unless breathed in quantity.
Red Chili Peppers
How about red chili pepper paste or hot curry paste? Spray it or mix it into a paste and put it on their trails.
Cinnamon from the spice rack is increasingly being used in garden insect control trials and products. You might find it of use to dust the outdoor nests. As an indoor natural ant control I don't know how it would work but you can only try. It would likely be more effective as a barrier to stop them from coming indoors so if you can sprinkle it around where you see them coming into the house, you'll likely have better results.
Black pepper has the same story as above. I can't vouch for either of these products. But if nothing else, your ants will have herbally spicy food to eat.
Bay leaves have been used for centuries for ant control. Put a leaf or two behind canisters on the counter, in your silver drawer, food shelves, anywhere ants have congregated. I haven't had the heart to take any leaves off my bay tree yet but this is reputed to work.
Whole cloves are supposed to do the same thing. They'd keep me away for sure.
Peppermint sprayed around the edges of your house and ant entry points will deter ants as will growing peppermint and other mints in your foundation planting. I caution you against this as you'll quickly be over-run with mint instead of ants. But spraying a mint extract or heavy mint tea might help; as long as it leaves a minty smell behind it is strong enough
So there's the word on natural ant control. Some of these will work better than others but at least you have the whole bag now. Good luck.