I have that type of ant on my KY ridgetop, and just leave them be down on the sloping woods below the yard. When they try moving into the yard, I do the gasoline method. It doesn't take much to burn out the nest. I'd first pull away some of the dry duff you have on yours. Wait a while for the chaos you create to calm down. Then wait briefly for the liquid to trickle down some ways into the tunnels and the fumes to fill the side tunnels. The fire is very satisfying and lasts longer than you would expect. It burns completely, so there is no worry about residual contamination. Don't overdo the gasoline - perhaps a cup to begin, and with that much, stand back! You can always do it again.
When they tried building right next to the pond and under the pond liner, I used boric acid, spread right over the entry holes. They track it into the nest and it gets consumed. No need to add sugar. It's difficult to find large containers of boric acid anymore. Try the hardware store. Don't buy the 4 oz. bottle for $7. You can buy it much cheaper elsewhere online.
ETA info I found from a pest control firm:
Boric acid is most often used in pesticides, and can be found in tablet form, liquid form, powder form and in various types of traps. It kills insects by absorbing into them, poisoning their stomachs, affecting their metabolism and abrading their exoskeletons. It’s far more likely to kill pests than borax is, due to its finer grain, which is harder for pests to detect and easier for them to ingest. When pests come into contact with it, whether through a trap or through walking across it a thin layer of it, it sticks to them, and they ingest it while cleaning themselves.