As far as I know, yeast helps the dough rise by eating away some of the sugar in the flour. But if we make low-carb bread (with, say, soya flour), yeast has nothing to eat and the bread will not rise. One solution might be to use baking powder, but then our bread has a cake-like texture. Do you have any suggestions? Thanks in advance.
As Bikeboy said, sugar will hasten the process, but yeast has enzymes that break down the starch to get to the sugar components.
If it has starch in it, yeast will eventually persevere and the dough will rise. It doesn't have to be wheat starch, but the yeasts we use commonly are used to working on wheat or barley flour. They will adapt to other starches. It may be better to make these breads on the sourdough principle, once you persuade a yeast to work.
If it takes longer than usual, you need to have patience ...
If you're worried about feeding the yeast, you'll probably want to add a little sugar to your recipe. If you keep the amount low enough (I'd probably start with half as much as would usually be used for a given amount of yeast) the yeast will consume all or nearly all of it.
As to cake-like texture, that's as much a factor of lack of gluten development as it is the leavening agent. If you don't have much gluten going, you get that crumbly cake or muffin texture--which is what you want in cakes or muffins.
If you're going to use very little wheat flour or none at all, you might consider adding vital wheat gluten to your recipe so that you can build a decent structure in your bread.
I imagine you'd have to make hundreds of loaves of bread to get the balances right on your own, so I'd recommend looking for low-carb yeast bread recipes that contain a bit of sugar and maybe vital wheat gluten. Those would probably have a decent chance of success.